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Introduction to Ring and Module Theory / / by Alberto Facchini
| Introduction to Ring and Module Theory / / by Alberto Facchini |
| Autore | Facchini Alberto |
| Edizione | [1st ed. 2025.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025 |
| Descrizione fisica | 1 online resource (440 pages) |
| Disciplina | 512.46 |
| Collana | Compact Textbooks in Mathematics |
| Soggetto topico |
Associative rings
Associative algebras Algebra, Homological Associative Rings and Algebras Category Theory, Homological Algebra Anells associatius Àlgebres associatives Àlgebra homològica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031825095
3031825098 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | - 1. Basic Notions -- 2. Some Classes of Modules -- 3. Right Artinian Rings -- 4. Local Rings, Injective Modules, Flat Modules -- 5. Additive Categories, Abelian Categories -- 6. Appendices. |
| Record Nr. | UNINA-9910992788803321 |
Facchini Alberto
|
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| Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno
| Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (424 pages) : illustrations |
| Disciplina | 512.4 |
| Collana | Springer INdAM |
| Soggetto topico |
PI-algebras
Anells associatius |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-63111-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- About the Editors -- Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras -- 1 Introduction -- 2 Finite Basis Problem -- 3 Engel Lie Algebras -- 3.1 Global Nilpotence -- 3.2 Restricted Burnside Problem: Local Nilpotence of Engel Lie algebras -- 4 Identities of Simple Lie Algebras -- 4.1 The Isomorphism Problem -- 4.2 Identities of Cartan Type Lie Algebras -- 4.3 Capelli Identities -- 5 Codimension Growth -- 5.1 Exponential Growth -- 5.2 Overexponential Growth -- 5.3 Colength -- 6 Graded Lie Algebras and Identities -- 7 Graded Identities of Lie Algebras and Generalizations -- 7.1 Codimension Growth -- 7.2 Isomorphism of H-Algebras -- 8 Special Lie Algebras -- References -- Minimal Degree of Identities of Matrix Algebras with Additional Structures -- 1 Introduction -- 2 Involution Case -- 3 Graded Case -- 4 Graded Involution Case -- References -- On the Asymptotics of Capelli Polynomials -- 1 Introduction -- 2 Ordinary Case -- 3 Z2-Graded Case -- 4 Involution Case -- 4.1 -Capelli Polynomials and the -Algebra UT(A1, ..., An) -- 4.2 Asymptotics for -Capelli Polynomials -- References -- Regev's Conjecture for Algebras with Hopf Actions -- 1 Introduction -- 2 Regev's Conjectures for Algebras Without Actions -- 2.1 Background on Magnums -- 2.2 Codimension Sequences -- 3 H-Cocharacters -- 4 Rationality of Poincaré Series -- 5 Young Derived Sequences -- References -- -Weak Identities and Central Polynomials for Matrices -- 1 Introduction -- 2 Preliminaries -- 2.1 Identities, Central Polynomials and Examples -- 2.2 Spechtian Polynomials -- 3 Weak Identities -- 3.1 Weak and Strong Variables -- 3.2 Modules of Weak Identities -- 4 Central Polynomials for Matrices -- 4.1 -Weak Central Polynomials -- 5 The Connection to the Representation Theory -- 5.1 Identities and the Group Algebra.
5.2 Identities and Representations -- 6 Weak Identities and the Case n = 2 -- 6.1 Polynomials of Degree m = 2 -- 6.2 Weak Identities of Degree m = 3 -- 6.3 Weak Identities of Degree m = 4 -- 7 The Weak PI-Degree of M3(F) -- 7.1 Fields of Characteristic Not 3 -- 7.2 The Case char F=3 -- 8 Weak Identities for M3(F) in Degree 6 -- 8.1 Weak Identities of M3(F) -- 8.2 Halpin's Identity and Its Projections -- 8.3 Identities from the Okubo Algebra -- 9 Matrices of Size n≥4 -- 9.1 Shadows of Identities -- 9.2 Weak Identities Degree 2n -- References -- Computing Multiplicities in the Sign Trace Cocharacters of M2,1(F) -- 1 Introduction -- 2 Reduced Notation -- 3 The Sign Trace Cocharacter of M2,1(F) -- 3.1 Computation of the Coefficient for {n-2,2} -- 4 The Final Result -- References -- b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings -- 1 Introduction -- 2 Some Results on Differential Identities with Automorphisms -- 3 Commuting Generalized Derivations and Commuting Generalized Skew Derivations -- 4 Some Remarks on Matrix Algebras -- 5 Commuting Inner b-Generalized Skew Derivations -- 6 Commuting b-Generalized Derivations on Multilinear Polynomials -- 7 The Main Result -- 7.1 Let d and δ be C-Linearly Independent Modulo SDint -- 7.2 Let d and δ be C-Linearly Dependent Modulo SDint -- 8 Some Open Problems -- References -- Relatively Free Algebras of Finite Rank -- 1 Introduction -- 2 Models for Relatively Free Algebras -- 3 General Remarks -- 4 Polynomial Identities for UT2(G(k)) -- 4.1 The Case UT2(G(2m)), for 1≤m≤2 -- 5 Polynomial Identities for Fk(UT2(G)) -- 6 Conclusion -- References -- Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals -- 1 Introduction -- 2 Growth of Algebras and Hilbert Series -- 3 Algebras with Prescribed Hilbert Series -- 4 PI-Algebras -- 5 Algebraic and Transcendental Power Series. 6 Planar Rooted Trees and Algebraic Series -- 7 Noncommutative Invariant Theory -- References -- Central Polynomials of Algebras and Their Growth -- 1 Introduction -- 2 A General Setting -- 3 Examples of Central Polynomials -- 4 Algebras Without Proper Central Polynomials -- 5 The Proper Central Exponent -- 6 The Central Exponent -- 7 Non Associative Algebras -- References -- Trace Identities on Diagonal Matrix Algebras -- 1 Introduction -- 2 Preliminaries -- 3 Matrix Algebras with Trace -- 4 Some Results on Dn -- 5 Trace Identities on D2 -- 6 Trace Identities on D3 -- References -- Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent -- 1 Introduction -- 2 Preliminaries -- 2.1 Generalities -- 2.2 Polynomial Identities -- 2.3 Multilinear Polynomials. Modules over the Symmetric Group -- 2.4 The Exponent -- 2.5 The Action of the General Linear Group -- 2.6 Special Pairs and Pairs of Associative Type -- 3 Polynomial Growth of the Codimensions -- 3.1 Slow Growth of the Codimensions -- 3.2 Characterizing Varieties of Pairs of Polynomial Growth -- 3.3 Almost Polynomial Growth -- 3.3.1 The Pair (UT2,UT2(-)) -- 3.3.2 The Pair (E,E(-)) -- 3.3.3 The Pair (M2,sl2) -- 3.3.4 More Examples -- 4 Graded Pairs and Amitsur's Conjecture -- 4.1 Weak Graded Polynomial Identities -- 4.2 Finitely Generated Superpairs -- 4.3 Non-integral Exponent: An Example -- References -- On Codimensions of Algebras with Involution -- 1 Introduction -- 2 *-Codimensions and *-Fundamental Algebras -- 3 Low Exponential Growth -- References -- Context-Free Languages and Associative Algebras with Algebraic Hilbert Series -- 1 Introduction -- 2 Preliminaries -- 2.1 Associative Algebras and Their Hilbert Series -- 2.2 The Homology and Hilbert Series of Monomial Algebras -- 2.3 Automaton Algebras and Homologically Unambiguous Algebras. 3 Finitely Presented Algebras Associated to Context-Free Languages -- 3.1 The General Construction -- 3.2 Graded Algebras Examples -- References -- On Almost Nilpotent Varieties of Linear Algebras -- 1 Introduction -- 2 Almost Nilpotent Varieties Generated by One or Two Dimensional Algebra -- 3 Almost Nilpotent Varieties and Skew Symmetric Polynomials -- 4 A Commutative Metabelian Algebra with Skew Symmetric Polynomials (a Jordan Algebra) -- 5 Anti-Commutative Metabelian Algebra with Skew Symmetric Polynomials -- 6 A Characterization of Almost Nilpotent Varieties in Different Classes of Algebras -- 7 An Infinite Series of Almost Nilpotent Metabelian Varieties with Polynomial Growth -- 8 Almost Nilpotent Varieties with Exponentional Growth -- References -- (δ,)-Differential Identities of UTm(F) -- 1 Introduction -- 2 The Problem -- 3 The Coupled Actions of δ and on UTm(F) -- 4 The Separate Actions of δ and on UTm(F) -- 5 Behind the Scenes -- References -- Identities in Group Rings, Enveloping Algebras and Poisson Algebras -- 1 Introduction -- 2 Identical Relations of Group Rings -- 3 Identical Relations of Enveloping Algebras -- 4 Poisson Algebras and Their Identities -- 4.1 Poisson Algebras -- 4.2 Examples of Poisson Algebras -- 4.3 Poisson Identities -- 5 Multilinear Identities of Symmetric Poisson Algebras -- 6 Lie Identities of Symmetric Poisson Algebras -- 6.1 Lie Nilpotence of Truncated Symmetric Algebras s(L) -- 6.2 Solvability of Truncated Symmetric Algebras s(L) -- 6.3 Nilpotency and Solvability of Symmetric Algebras S(L) -- 6.4 Delta-Sets and Multilinear Poisson Identical Relations -- 6.5 Products of Commutators in Poisson Algebras -- 6.6 Solvability of Symmetric Algebras s(L) and S(L) in Case Char K = 2 -- References -- Notes on the History of Identities on Group (and Loop) Algebras -- 1 Introduction. 2 Existence of Polynomial Identities -- 3 Group Theoretical Properties of Unit Groups -- 4 Group Indentities -- 5 Loop Algebras -- References -- Cayley Hamilton Algebras -- 1 Introduction -- 2 The Cayley-Hamilton Identity -- 3 The First and Second Fundamental Theorem -- 3.1 The Free Trace Algebra -- 3.3 A Characteristic Free Approach -- 3.12 Symbolic Approach -- 3.12.1 The Approach of Zieplies and Vaccarino -- References -- Growth of Differential Identities -- 1 Introduction -- 2 L-Algebras and Differential Identities -- 3 On Algebras with Derivations of Polynomial Growth -- 4 The Algebra of 2 x 2 Upper Triangular Matrices and Its Differential Identities -- 5 On Differential Identities of the Grassmann Algebra -- References -- Derived Lengths of Symmetric Poisson Algebras -- 1 Introduction -- 2 Definitions and Notation -- 3 The Lie Structure of Enveloping Algebras -- 4 Symmetric Poisson Algebras Satisfying a Poisson Identity -- 5 Lie Nilpotence and Solvability of S(L) and s(L) -- 6 Derived Lengths of s(L) -- References -- Group and Polynomial Identities in Group Rings -- 1 Introduction -- 2 -Group Identities for U(FG) -- 3 Group Identities for Unitary Units of FG -- References. |
| Record Nr. | UNISA-996466544303316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno
| Polynomial identities in algebras / / edited by Onofrio Mario Di Vincenzo and Antonio Giambruno |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (424 pages) : illustrations |
| Disciplina | 512.4 |
| Collana | Springer INdAM |
| Soggetto topico |
PI-algebras
Anells associatius |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-63111-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- About the Editors -- Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras -- 1 Introduction -- 2 Finite Basis Problem -- 3 Engel Lie Algebras -- 3.1 Global Nilpotence -- 3.2 Restricted Burnside Problem: Local Nilpotence of Engel Lie algebras -- 4 Identities of Simple Lie Algebras -- 4.1 The Isomorphism Problem -- 4.2 Identities of Cartan Type Lie Algebras -- 4.3 Capelli Identities -- 5 Codimension Growth -- 5.1 Exponential Growth -- 5.2 Overexponential Growth -- 5.3 Colength -- 6 Graded Lie Algebras and Identities -- 7 Graded Identities of Lie Algebras and Generalizations -- 7.1 Codimension Growth -- 7.2 Isomorphism of H-Algebras -- 8 Special Lie Algebras -- References -- Minimal Degree of Identities of Matrix Algebras with Additional Structures -- 1 Introduction -- 2 Involution Case -- 3 Graded Case -- 4 Graded Involution Case -- References -- On the Asymptotics of Capelli Polynomials -- 1 Introduction -- 2 Ordinary Case -- 3 Z2-Graded Case -- 4 Involution Case -- 4.1 -Capelli Polynomials and the -Algebra UT(A1, ..., An) -- 4.2 Asymptotics for -Capelli Polynomials -- References -- Regev's Conjecture for Algebras with Hopf Actions -- 1 Introduction -- 2 Regev's Conjectures for Algebras Without Actions -- 2.1 Background on Magnums -- 2.2 Codimension Sequences -- 3 H-Cocharacters -- 4 Rationality of Poincaré Series -- 5 Young Derived Sequences -- References -- -Weak Identities and Central Polynomials for Matrices -- 1 Introduction -- 2 Preliminaries -- 2.1 Identities, Central Polynomials and Examples -- 2.2 Spechtian Polynomials -- 3 Weak Identities -- 3.1 Weak and Strong Variables -- 3.2 Modules of Weak Identities -- 4 Central Polynomials for Matrices -- 4.1 -Weak Central Polynomials -- 5 The Connection to the Representation Theory -- 5.1 Identities and the Group Algebra.
5.2 Identities and Representations -- 6 Weak Identities and the Case n = 2 -- 6.1 Polynomials of Degree m = 2 -- 6.2 Weak Identities of Degree m = 3 -- 6.3 Weak Identities of Degree m = 4 -- 7 The Weak PI-Degree of M3(F) -- 7.1 Fields of Characteristic Not 3 -- 7.2 The Case char F=3 -- 8 Weak Identities for M3(F) in Degree 6 -- 8.1 Weak Identities of M3(F) -- 8.2 Halpin's Identity and Its Projections -- 8.3 Identities from the Okubo Algebra -- 9 Matrices of Size n≥4 -- 9.1 Shadows of Identities -- 9.2 Weak Identities Degree 2n -- References -- Computing Multiplicities in the Sign Trace Cocharacters of M2,1(F) -- 1 Introduction -- 2 Reduced Notation -- 3 The Sign Trace Cocharacter of M2,1(F) -- 3.1 Computation of the Coefficient for {n-2,2} -- 4 The Final Result -- References -- b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings -- 1 Introduction -- 2 Some Results on Differential Identities with Automorphisms -- 3 Commuting Generalized Derivations and Commuting Generalized Skew Derivations -- 4 Some Remarks on Matrix Algebras -- 5 Commuting Inner b-Generalized Skew Derivations -- 6 Commuting b-Generalized Derivations on Multilinear Polynomials -- 7 The Main Result -- 7.1 Let d and δ be C-Linearly Independent Modulo SDint -- 7.2 Let d and δ be C-Linearly Dependent Modulo SDint -- 8 Some Open Problems -- References -- Relatively Free Algebras of Finite Rank -- 1 Introduction -- 2 Models for Relatively Free Algebras -- 3 General Remarks -- 4 Polynomial Identities for UT2(G(k)) -- 4.1 The Case UT2(G(2m)), for 1≤m≤2 -- 5 Polynomial Identities for Fk(UT2(G)) -- 6 Conclusion -- References -- Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals -- 1 Introduction -- 2 Growth of Algebras and Hilbert Series -- 3 Algebras with Prescribed Hilbert Series -- 4 PI-Algebras -- 5 Algebraic and Transcendental Power Series. 6 Planar Rooted Trees and Algebraic Series -- 7 Noncommutative Invariant Theory -- References -- Central Polynomials of Algebras and Their Growth -- 1 Introduction -- 2 A General Setting -- 3 Examples of Central Polynomials -- 4 Algebras Without Proper Central Polynomials -- 5 The Proper Central Exponent -- 6 The Central Exponent -- 7 Non Associative Algebras -- References -- Trace Identities on Diagonal Matrix Algebras -- 1 Introduction -- 2 Preliminaries -- 3 Matrix Algebras with Trace -- 4 Some Results on Dn -- 5 Trace Identities on D2 -- 6 Trace Identities on D3 -- References -- Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent -- 1 Introduction -- 2 Preliminaries -- 2.1 Generalities -- 2.2 Polynomial Identities -- 2.3 Multilinear Polynomials. Modules over the Symmetric Group -- 2.4 The Exponent -- 2.5 The Action of the General Linear Group -- 2.6 Special Pairs and Pairs of Associative Type -- 3 Polynomial Growth of the Codimensions -- 3.1 Slow Growth of the Codimensions -- 3.2 Characterizing Varieties of Pairs of Polynomial Growth -- 3.3 Almost Polynomial Growth -- 3.3.1 The Pair (UT2,UT2(-)) -- 3.3.2 The Pair (E,E(-)) -- 3.3.3 The Pair (M2,sl2) -- 3.3.4 More Examples -- 4 Graded Pairs and Amitsur's Conjecture -- 4.1 Weak Graded Polynomial Identities -- 4.2 Finitely Generated Superpairs -- 4.3 Non-integral Exponent: An Example -- References -- On Codimensions of Algebras with Involution -- 1 Introduction -- 2 *-Codimensions and *-Fundamental Algebras -- 3 Low Exponential Growth -- References -- Context-Free Languages and Associative Algebras with Algebraic Hilbert Series -- 1 Introduction -- 2 Preliminaries -- 2.1 Associative Algebras and Their Hilbert Series -- 2.2 The Homology and Hilbert Series of Monomial Algebras -- 2.3 Automaton Algebras and Homologically Unambiguous Algebras. 3 Finitely Presented Algebras Associated to Context-Free Languages -- 3.1 The General Construction -- 3.2 Graded Algebras Examples -- References -- On Almost Nilpotent Varieties of Linear Algebras -- 1 Introduction -- 2 Almost Nilpotent Varieties Generated by One or Two Dimensional Algebra -- 3 Almost Nilpotent Varieties and Skew Symmetric Polynomials -- 4 A Commutative Metabelian Algebra with Skew Symmetric Polynomials (a Jordan Algebra) -- 5 Anti-Commutative Metabelian Algebra with Skew Symmetric Polynomials -- 6 A Characterization of Almost Nilpotent Varieties in Different Classes of Algebras -- 7 An Infinite Series of Almost Nilpotent Metabelian Varieties with Polynomial Growth -- 8 Almost Nilpotent Varieties with Exponentional Growth -- References -- (δ,)-Differential Identities of UTm(F) -- 1 Introduction -- 2 The Problem -- 3 The Coupled Actions of δ and on UTm(F) -- 4 The Separate Actions of δ and on UTm(F) -- 5 Behind the Scenes -- References -- Identities in Group Rings, Enveloping Algebras and Poisson Algebras -- 1 Introduction -- 2 Identical Relations of Group Rings -- 3 Identical Relations of Enveloping Algebras -- 4 Poisson Algebras and Their Identities -- 4.1 Poisson Algebras -- 4.2 Examples of Poisson Algebras -- 4.3 Poisson Identities -- 5 Multilinear Identities of Symmetric Poisson Algebras -- 6 Lie Identities of Symmetric Poisson Algebras -- 6.1 Lie Nilpotence of Truncated Symmetric Algebras s(L) -- 6.2 Solvability of Truncated Symmetric Algebras s(L) -- 6.3 Nilpotency and Solvability of Symmetric Algebras S(L) -- 6.4 Delta-Sets and Multilinear Poisson Identical Relations -- 6.5 Products of Commutators in Poisson Algebras -- 6.6 Solvability of Symmetric Algebras s(L) and S(L) in Case Char K = 2 -- References -- Notes on the History of Identities on Group (and Loop) Algebras -- 1 Introduction. 2 Existence of Polynomial Identities -- 3 Group Theoretical Properties of Unit Groups -- 4 Group Indentities -- 5 Loop Algebras -- References -- Cayley Hamilton Algebras -- 1 Introduction -- 2 The Cayley-Hamilton Identity -- 3 The First and Second Fundamental Theorem -- 3.1 The Free Trace Algebra -- 3.3 A Characteristic Free Approach -- 3.12 Symbolic Approach -- 3.12.1 The Approach of Zieplies and Vaccarino -- References -- Growth of Differential Identities -- 1 Introduction -- 2 L-Algebras and Differential Identities -- 3 On Algebras with Derivations of Polynomial Growth -- 4 The Algebra of 2 x 2 Upper Triangular Matrices and Its Differential Identities -- 5 On Differential Identities of the Grassmann Algebra -- References -- Derived Lengths of Symmetric Poisson Algebras -- 1 Introduction -- 2 Definitions and Notation -- 3 The Lie Structure of Enveloping Algebras -- 4 Symmetric Poisson Algebras Satisfying a Poisson Identity -- 5 Lie Nilpotence and Solvability of S(L) and s(L) -- 6 Derived Lengths of s(L) -- References -- Group and Polynomial Identities in Group Rings -- 1 Introduction -- 2 -Group Identities for U(FG) -- 3 Group Identities for Unitary Units of FG -- References. |
| Record Nr. | UNINA-9910484534203321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The theory of near-rings / / Robert Lockhart
| The theory of near-rings / / Robert Lockhart |
| Autore | Lockhart Robert (Mathematician) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (555 pages) |
| Disciplina | 512.4 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Near-rings
Anells associatius |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030817558
9783030817541 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword by Günter Pilz -- Preface -- Notation -- Gothic Symbols -- Contents -- Part I Structure Theory -- 1 Stems, Mappings and Near-Rings -- 1.1 Basic Group Theory -- 1.1.1 Sylow Theory -- 1.1.2 The Jordan-Hölder Theorem -- 1.1.3 Solvable, Supersolvable and Nilpotent Groups -- 1.2 Homological Algebra and Category Theory -- 1.3 Topology -- 1.3.1 The Kuratowski Closure Axioms -- 1.4 Stems and Near-Rings -- 1.4.1 Star Notation -- 1.4.2 Pre-Near-Rings -- 1.4.3 Conventions and Notation -- 1.4.4 Examples of p.n.r. and of Near-Rings -- 1.5 Hosting -- 1.6 Ideals -- 1.7 Subdirect Products of Near-Rings -- 1.8 Sideals and Near-Ring Groups -- 1.8.1 Generalisations -- 1.8.2 Right Near-Ring Groups -- 1.8.3 Highly Non-standard Terminology -- 1.8.4 Sub-Structures and Mideals -- 1.8.5 Faithfulness -- 1.8.6 Monogenicity -- 1.8.7 Some Two-Sided Sideals -- 1.8.8 The Weak Left Ideal Property -- 1.8.9 Rings and Modules -- 1.9 Semi-simplicity -- 1.10 Prime and Semi-prime Ideals -- 1.10.1 Prime Ideals -- 1.10.2 Semi-prime Ideals -- 1.10.3 Complements of Prime and Semi-prime Ideals -- 1.10.4 Prime and Semi-prime Ideals -- 1.11 Near-Fields -- 1.12 A-Matrices -- 1.13 Functions and Function Composition -- 1.14 The δ Operator and Phomomorphisms -- 1.14.1 The δ Operator -- 1.14.2 Phomomorphisms -- 1.15 Annihilators -- 1.16 Conjugacy and Annihilators -- 1.17 Sylow Subgroups -- 1.18 The Zeroiser Ideal -- 1.19 The Core of a Left Ideal -- 1.20 Anti-chains of Subgroups -- 1.21 Subsets -- 1.21.1 Generating Near-Rings -- 1.21.2 Lifting Near-Rings -- 1.22 Nil and Nilpotent Sets -- 1.22.1 Sums of Nil Ideals -- 1.22.2 Sums of Nilpotent Ideals -- 1.23 Cores -- 1.24 Classes of Near-Rings -- 1.24.1 Distributively Generated and F-Near-Rings -- 1.24.2 Class F Near-Rings -- 1.24.3 The Fj Cores, (j = 1,2, 3) -- 1.24.4 Constant and Near-Constant Near-Rings -- 1.24.5 Opposites.
1.24.6 Non-Zero-Symmetric Near-Rings -- 1.25 The Distributor and the Annular Ideal -- 1.25.1 The Distributor Ideal -- 1.25.2 The Multiplicative Centre -- 1.25.3 The Annular Ideal -- 1.26 Bi-distributive Stems -- 1.27 Subgroup Series -- 1.27.1 Weak Distributivity -- 1.27.2 Annularity -- 1.27.3 N(+)-Nilpotence -- 1.28 Modular Ideals -- 1.29 Quasi-regular Left Ideals -- 1.29.1 Quasi-regularity in Rings -- 1.30 Pseudo-Rings -- 1.31 Propriety -- 1.31.1 ``Left'' and ``Right'' Confusion -- 1.31.2 Proper Structures -- 1.31.3 Transferred Epithets -- 1.31.4 Problematic Terminology -- 1.32 An Unsettling Homomorphism -- 2 Near-Ring Theory -- 2.1 Pre-Near-Ring Construction Conditions and the Associativity Core -- 2.1.1 Host Determination Strategies -- 2.1.2 Distributive Generation -- 2.1.3 Co-structures: A Sort of Duality -- 2.1.4 Reduced Free Groups and Another Sort of Duality -- 2.1.5 Construction Conditions and F-Near-Rings -- 2.1.6 Bounds on Associativity Checking -- 2.2 Coupling and Dickson Near-Rings -- 2.2.1 D-Near-Rings -- 2.3 Affine Near-Rings -- 2.4 Near-Rings Hosted by Semi-direct Products -- 2.4.1 Near-Rings Hosted by Dn -- 2.5 Ideas from Mathematical Logic and Universal Algebra -- 2.5.1 Equational Products -- 2.5.2 Boolean Algebras and Boolean Rings -- 2.5.3 Boolean Near-Rings -- 2.5.4 Finite Boolean Near-Rings -- 2.5.5 Partially Ordered Sets -- 2.5.6 Lattices -- 2.5.7 Finiteness Conditions: Chains, Intersections, Generators -- 2.5.8 Ultra-Products -- 2.6 Adjoining an Identity -- 2.7 Planarity -- 2.7.1 The Ferrero Construction -- 3 Near-Fields -- 3.1 Near-Fields -- 3.1.1 Near-Fields Not of Characteristic 2 -- 3.1.2 General Near-Fields -- 3.2 Commutators and the Sub-near-Field L -- 3.2.1 The Sub-near-Field F -- 3.3 Finite Near-Fields -- 3.3.1 The Smallest Proper Near-Field -- 3.3.2 General Cases -- 3.3.3 The Normal Core of D*. 3.3.4 The Multiplicative Centre -- 3.3.5 The Multiplicative Group Structure of Finite Near-Fields -- 3.3.6 Presentations for Finite Near-Fields with S2 Cyclic -- 3.3.7 Z-Group Properties -- 3.3.8 The Product of All the Non-zero Elements -- 3.4 Finite Dickson Near-Fields -- 3.4.1 Coupling Maps and Dickson Near-Fields -- 3.4.2 A Theorem Reported by Marshall Hall -- 3.4.3 The Smallest Proper Near-Field Having All Sylow Subgroups Cyclic -- 3.4.4 The Algebra of the Dickson Process -- 3.4.5 A Generalisation of the Dickson Process -- 3.4.6 The Historical Dickson Process -- 3.4.7 When N* Is a Z-Group -- 3.4.8 Multiplication in Finite Dickson Near-Fields -- 3.4.9 Isomorphism in Finite Dickson Near-Fields -- 3.4.10 Sub-near-Fields -- 3.4.11 Number-Theoretic Issues -- 3.4.12 Near-Field Automorphisms -- 3.4.13 Prime Divisors of δ: Hall's Theorem -- 3.4.14 L and N -- 3.4.15 An Intrinsic Characterisation of Dickson Near-Fields -- 3.5 Group Structure of N* -- 3.5.1 Presentations for Solvable Near-Fields with S2 Quaternionic -- 3.5.2 Presentation for Non-Dickson Solvable Cases -- 3.6 Frobenius Groups -- 3.6.1 Basics -- 3.6.2 Sharply 2-Transitive Groups -- 3.6.3 Affine Groups -- 3.6.4 Near-Fields to Sharply 2-Transitive Groups -- 3.6.5 Further Affine Groups -- 3.6.6 Sharply 2-Transitive Groups to Near-Fields -- 3.6.7 Dickson and Non-Dickson Near-Fields -- 3.7 Finite Non-Dickson Near-Fields -- 3.7.1 A Classification Lemma -- 3.7.2 Element Orders -- 3.8 General Finite Non-fields -- 3.9 Infinite Near-Fields -- 3.9.1 Characteristic Zero -- 3.10 A Continuing Story -- Part II Near-Rings Hosted by Classes of Groups -- 4 Near-Rings on Groups with Low Order -- 4.1 Small Non-abelian Groups -- 4.1.1 Groups with Order 16 -- 4.1.2 Groups with Order 18 -- 4.1.3 Non-abelian Groups with Order 21 -- 4.1.4 Groups with Order 24 -- 4.1.5 Groups with Order 27 -- 4.1.6 Coda. 5 Near-Rings on Some Families of Groups -- 5.1 Finite Symmetric Groups -- 5.2 Finite Simple Non-abelian Groups -- 5.2.1 Isotopy -- 5.2.2 A Class of Non-trivial Near-Rings Hosted by Any Group -- 5.3 Unital Near-Rings on Sn -- 5.4 The Quaternion Group with Order 8 -- 5.4.1 Unital d.g. p.n.r. Hosted by Q8 -- 5.5 Dihedral Groups -- 5.5.1 The Dihedral Group of Order 8 -- 5.5.2 Other Finite Dihedral Groups -- 5.5.3 Pre-Near-Rings -- 5.5.4 The Infinite Dihedral Group -- 5.6 Finite Groups from the Krimmel Class -- 5.6.1 A Classification Theorem Reported in Gorenstein -- 5.7 Generalised Quaternion Groups -- 5.8 Dicyclic Groups -- 5.9 Finite Hamiltonian Groups -- 5.10 Semi-dihedral Groups -- 5.11 Gorenstein's Group Mm(p) -- 5.12 Central Products -- 5.13 Free Products -- 5.14 Finite Non-solvable Groups -- 5.14.1 Groups with Order 360 -- 5.14.2 Groups with Order 600 -- 5.14.3 Groups with Order 720 -- 5.14.4 Remaining Possibilities with Order 720 -- 5.14.5 Direct Sums of Simple Groups -- 6 Near-Rings Hosted by p-Groups and Related Groups -- 6.1 Groups with Order p -- 6.2 The Klein Group -- 6.3 Groups with Order 2p (p > -- 2) -- 6.4 Groups with Order pq Where p and q Are Prime and (p < -- q) -- 6.5 Groups with Order p2 -- 6.6 Groups with Order 2p2 (p > -- 2) -- 6.7 Groups with Order p3 (p > -- 2) -- 6.8 Groups with Order 2p3 or Order 2p4 (p > -- 2) -- 6.9 Groups with Order p4 (p > -- 2) -- 6.10 The Prüfer Groups -- 6.11 A Research Suggestion -- Part III Representations and Cohomology -- 7 Transformation Near-Rings -- 7.1 Introduction -- 7.2 Preliminaries -- 7.2.1 Mapping Notation -- 7.2.2 Ideals of T(N) -- 7.2.3 Automorphisms of T(N) -- 7.2.4 The Finite Topology -- 7.2.5 Sub-near-Rings -- 7.2.6 E(N), I(N), A(N), B(N), and Phom(N) -- 7.3 Multiplicative Structure -- 7.3.1 Sideals and Cleiks -- 7.3.2 A-Matrices -- 7.3.3 Operating on (a,b). 7.3.4 Left and Right Sideals -- 7.3.5 Nilpotence -- 7.3.6 Idempotence -- 7.3.7 T0(N) Generalised -- 7.3.8 A Sub-near-Ring of T0(S3) -- 7.4 T(N), H(N) and B(N) -- 7.4.1 The Structure of H(N) -- 7.4.2 The Structure of T(N) -- 7.4.3 More on the Representation -- 7.4.4 Permutations and Additive Isomorphisms -- 7.4.5 Automorphisms of T0(N) -- 7.4.6 The Structure of B(N) -- 7.4.7 Further Investigation -- 7.5 Some Examples -- 7.5.1 The Cyclic Group C3 -- 7.5.2 Finite Dihedral Groups -- 7.5.3 Dn when n Is Odd -- 7.5.4 Dn when n Is Even -- 7.5.5 D∞ and A(D∞) -- 7.5.6 Q8 -- 7.6 Additive Structure -- 7.6.1 M(N) -- 7.6.2 Centraliser Near-Rings -- 7.6.3 A Duality of Semi-Groups -- 7.6.4 Density -- 7.7 MS() when S Is Fixed-Point-Free -- 7.7.1 The Structure of Minimal Left Ideals -- 7.7.2 Right Near-Ring Groups -- 7.7.3 Annihilators -- 7.7.4 Chains of Left Ideals -- 7.7.5 Simple Near-Rings -- 7.7.6 Left Ideals -- 7.7.7 Modular Left Ideals -- 8 Generalisations and Sub-near-Rings of Transformation Near-Rings -- 8.1 Commutators -- 8.2 More Sub-near-Rings -- 8.2.1 Special Cases -- 8.3 Hadamard Products -- 8.4 Endomorphism Near-Rings -- 8.4.1 Related Sub-near-Rings -- 8.4.2 Sequences of Endomorphism Near-Rings -- 8.5 Other Kinds of Endomorphism Near-Ring -- 8.6 Change of Groups -- 8.6.1 Near-Loops -- 8.6.2 Homomorphisms and Normal Sub-Loops -- 8.6.3 The Host Problem -- 8.6.4 Transformations on Near-Loops -- 8.6.5 Transformations on Sets -- 8.7 The Stemhome Near-Ring -- 8.7.1 The Stemhome Functor -- 8.8 The Wurzel -- 8.9 Elementary Closure Procedures -- 8.9.1 Additive and Multiplicative Closures -- 8.9.2 A Topological Closure -- 8.10 Polynomials -- 8.10.1 Near-Rings -- 8.10.2 Skew Polynomial Near-Rings -- 9 Phomomorphisms -- 9.1 General Theory -- 9.1.1 Extending Mappings to Phomomorphisms -- 9.1.2 Phomomorphism-Invariant Subgroups -- 9.2 Cohomology Groups. 9.2.1 Non-abelian Group Cohomology. |
| Record Nr. | UNINA-9910508454403321 |
|
Lockhart Robert (Mathematician)
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The theory of near-rings / / Robert Lockhart
| The theory of near-rings / / Robert Lockhart |
| Autore | Lockhart Robert (Mathematician) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (555 pages) |
| Disciplina | 512.4 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Near-rings
Anells associatius |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030817558
9783030817541 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword by Günter Pilz -- Preface -- Notation -- Gothic Symbols -- Contents -- Part I Structure Theory -- 1 Stems, Mappings and Near-Rings -- 1.1 Basic Group Theory -- 1.1.1 Sylow Theory -- 1.1.2 The Jordan-Hölder Theorem -- 1.1.3 Solvable, Supersolvable and Nilpotent Groups -- 1.2 Homological Algebra and Category Theory -- 1.3 Topology -- 1.3.1 The Kuratowski Closure Axioms -- 1.4 Stems and Near-Rings -- 1.4.1 Star Notation -- 1.4.2 Pre-Near-Rings -- 1.4.3 Conventions and Notation -- 1.4.4 Examples of p.n.r. and of Near-Rings -- 1.5 Hosting -- 1.6 Ideals -- 1.7 Subdirect Products of Near-Rings -- 1.8 Sideals and Near-Ring Groups -- 1.8.1 Generalisations -- 1.8.2 Right Near-Ring Groups -- 1.8.3 Highly Non-standard Terminology -- 1.8.4 Sub-Structures and Mideals -- 1.8.5 Faithfulness -- 1.8.6 Monogenicity -- 1.8.7 Some Two-Sided Sideals -- 1.8.8 The Weak Left Ideal Property -- 1.8.9 Rings and Modules -- 1.9 Semi-simplicity -- 1.10 Prime and Semi-prime Ideals -- 1.10.1 Prime Ideals -- 1.10.2 Semi-prime Ideals -- 1.10.3 Complements of Prime and Semi-prime Ideals -- 1.10.4 Prime and Semi-prime Ideals -- 1.11 Near-Fields -- 1.12 A-Matrices -- 1.13 Functions and Function Composition -- 1.14 The δ Operator and Phomomorphisms -- 1.14.1 The δ Operator -- 1.14.2 Phomomorphisms -- 1.15 Annihilators -- 1.16 Conjugacy and Annihilators -- 1.17 Sylow Subgroups -- 1.18 The Zeroiser Ideal -- 1.19 The Core of a Left Ideal -- 1.20 Anti-chains of Subgroups -- 1.21 Subsets -- 1.21.1 Generating Near-Rings -- 1.21.2 Lifting Near-Rings -- 1.22 Nil and Nilpotent Sets -- 1.22.1 Sums of Nil Ideals -- 1.22.2 Sums of Nilpotent Ideals -- 1.23 Cores -- 1.24 Classes of Near-Rings -- 1.24.1 Distributively Generated and F-Near-Rings -- 1.24.2 Class F Near-Rings -- 1.24.3 The Fj Cores, (j = 1,2, 3) -- 1.24.4 Constant and Near-Constant Near-Rings -- 1.24.5 Opposites.
1.24.6 Non-Zero-Symmetric Near-Rings -- 1.25 The Distributor and the Annular Ideal -- 1.25.1 The Distributor Ideal -- 1.25.2 The Multiplicative Centre -- 1.25.3 The Annular Ideal -- 1.26 Bi-distributive Stems -- 1.27 Subgroup Series -- 1.27.1 Weak Distributivity -- 1.27.2 Annularity -- 1.27.3 N(+)-Nilpotence -- 1.28 Modular Ideals -- 1.29 Quasi-regular Left Ideals -- 1.29.1 Quasi-regularity in Rings -- 1.30 Pseudo-Rings -- 1.31 Propriety -- 1.31.1 ``Left'' and ``Right'' Confusion -- 1.31.2 Proper Structures -- 1.31.3 Transferred Epithets -- 1.31.4 Problematic Terminology -- 1.32 An Unsettling Homomorphism -- 2 Near-Ring Theory -- 2.1 Pre-Near-Ring Construction Conditions and the Associativity Core -- 2.1.1 Host Determination Strategies -- 2.1.2 Distributive Generation -- 2.1.3 Co-structures: A Sort of Duality -- 2.1.4 Reduced Free Groups and Another Sort of Duality -- 2.1.5 Construction Conditions and F-Near-Rings -- 2.1.6 Bounds on Associativity Checking -- 2.2 Coupling and Dickson Near-Rings -- 2.2.1 D-Near-Rings -- 2.3 Affine Near-Rings -- 2.4 Near-Rings Hosted by Semi-direct Products -- 2.4.1 Near-Rings Hosted by Dn -- 2.5 Ideas from Mathematical Logic and Universal Algebra -- 2.5.1 Equational Products -- 2.5.2 Boolean Algebras and Boolean Rings -- 2.5.3 Boolean Near-Rings -- 2.5.4 Finite Boolean Near-Rings -- 2.5.5 Partially Ordered Sets -- 2.5.6 Lattices -- 2.5.7 Finiteness Conditions: Chains, Intersections, Generators -- 2.5.8 Ultra-Products -- 2.6 Adjoining an Identity -- 2.7 Planarity -- 2.7.1 The Ferrero Construction -- 3 Near-Fields -- 3.1 Near-Fields -- 3.1.1 Near-Fields Not of Characteristic 2 -- 3.1.2 General Near-Fields -- 3.2 Commutators and the Sub-near-Field L -- 3.2.1 The Sub-near-Field F -- 3.3 Finite Near-Fields -- 3.3.1 The Smallest Proper Near-Field -- 3.3.2 General Cases -- 3.3.3 The Normal Core of D*. 3.3.4 The Multiplicative Centre -- 3.3.5 The Multiplicative Group Structure of Finite Near-Fields -- 3.3.6 Presentations for Finite Near-Fields with S2 Cyclic -- 3.3.7 Z-Group Properties -- 3.3.8 The Product of All the Non-zero Elements -- 3.4 Finite Dickson Near-Fields -- 3.4.1 Coupling Maps and Dickson Near-Fields -- 3.4.2 A Theorem Reported by Marshall Hall -- 3.4.3 The Smallest Proper Near-Field Having All Sylow Subgroups Cyclic -- 3.4.4 The Algebra of the Dickson Process -- 3.4.5 A Generalisation of the Dickson Process -- 3.4.6 The Historical Dickson Process -- 3.4.7 When N* Is a Z-Group -- 3.4.8 Multiplication in Finite Dickson Near-Fields -- 3.4.9 Isomorphism in Finite Dickson Near-Fields -- 3.4.10 Sub-near-Fields -- 3.4.11 Number-Theoretic Issues -- 3.4.12 Near-Field Automorphisms -- 3.4.13 Prime Divisors of δ: Hall's Theorem -- 3.4.14 L and N -- 3.4.15 An Intrinsic Characterisation of Dickson Near-Fields -- 3.5 Group Structure of N* -- 3.5.1 Presentations for Solvable Near-Fields with S2 Quaternionic -- 3.5.2 Presentation for Non-Dickson Solvable Cases -- 3.6 Frobenius Groups -- 3.6.1 Basics -- 3.6.2 Sharply 2-Transitive Groups -- 3.6.3 Affine Groups -- 3.6.4 Near-Fields to Sharply 2-Transitive Groups -- 3.6.5 Further Affine Groups -- 3.6.6 Sharply 2-Transitive Groups to Near-Fields -- 3.6.7 Dickson and Non-Dickson Near-Fields -- 3.7 Finite Non-Dickson Near-Fields -- 3.7.1 A Classification Lemma -- 3.7.2 Element Orders -- 3.8 General Finite Non-fields -- 3.9 Infinite Near-Fields -- 3.9.1 Characteristic Zero -- 3.10 A Continuing Story -- Part II Near-Rings Hosted by Classes of Groups -- 4 Near-Rings on Groups with Low Order -- 4.1 Small Non-abelian Groups -- 4.1.1 Groups with Order 16 -- 4.1.2 Groups with Order 18 -- 4.1.3 Non-abelian Groups with Order 21 -- 4.1.4 Groups with Order 24 -- 4.1.5 Groups with Order 27 -- 4.1.6 Coda. 5 Near-Rings on Some Families of Groups -- 5.1 Finite Symmetric Groups -- 5.2 Finite Simple Non-abelian Groups -- 5.2.1 Isotopy -- 5.2.2 A Class of Non-trivial Near-Rings Hosted by Any Group -- 5.3 Unital Near-Rings on Sn -- 5.4 The Quaternion Group with Order 8 -- 5.4.1 Unital d.g. p.n.r. Hosted by Q8 -- 5.5 Dihedral Groups -- 5.5.1 The Dihedral Group of Order 8 -- 5.5.2 Other Finite Dihedral Groups -- 5.5.3 Pre-Near-Rings -- 5.5.4 The Infinite Dihedral Group -- 5.6 Finite Groups from the Krimmel Class -- 5.6.1 A Classification Theorem Reported in Gorenstein -- 5.7 Generalised Quaternion Groups -- 5.8 Dicyclic Groups -- 5.9 Finite Hamiltonian Groups -- 5.10 Semi-dihedral Groups -- 5.11 Gorenstein's Group Mm(p) -- 5.12 Central Products -- 5.13 Free Products -- 5.14 Finite Non-solvable Groups -- 5.14.1 Groups with Order 360 -- 5.14.2 Groups with Order 600 -- 5.14.3 Groups with Order 720 -- 5.14.4 Remaining Possibilities with Order 720 -- 5.14.5 Direct Sums of Simple Groups -- 6 Near-Rings Hosted by p-Groups and Related Groups -- 6.1 Groups with Order p -- 6.2 The Klein Group -- 6.3 Groups with Order 2p (p > -- 2) -- 6.4 Groups with Order pq Where p and q Are Prime and (p < -- q) -- 6.5 Groups with Order p2 -- 6.6 Groups with Order 2p2 (p > -- 2) -- 6.7 Groups with Order p3 (p > -- 2) -- 6.8 Groups with Order 2p3 or Order 2p4 (p > -- 2) -- 6.9 Groups with Order p4 (p > -- 2) -- 6.10 The Prüfer Groups -- 6.11 A Research Suggestion -- Part III Representations and Cohomology -- 7 Transformation Near-Rings -- 7.1 Introduction -- 7.2 Preliminaries -- 7.2.1 Mapping Notation -- 7.2.2 Ideals of T(N) -- 7.2.3 Automorphisms of T(N) -- 7.2.4 The Finite Topology -- 7.2.5 Sub-near-Rings -- 7.2.6 E(N), I(N), A(N), B(N), and Phom(N) -- 7.3 Multiplicative Structure -- 7.3.1 Sideals and Cleiks -- 7.3.2 A-Matrices -- 7.3.3 Operating on (a,b). 7.3.4 Left and Right Sideals -- 7.3.5 Nilpotence -- 7.3.6 Idempotence -- 7.3.7 T0(N) Generalised -- 7.3.8 A Sub-near-Ring of T0(S3) -- 7.4 T(N), H(N) and B(N) -- 7.4.1 The Structure of H(N) -- 7.4.2 The Structure of T(N) -- 7.4.3 More on the Representation -- 7.4.4 Permutations and Additive Isomorphisms -- 7.4.5 Automorphisms of T0(N) -- 7.4.6 The Structure of B(N) -- 7.4.7 Further Investigation -- 7.5 Some Examples -- 7.5.1 The Cyclic Group C3 -- 7.5.2 Finite Dihedral Groups -- 7.5.3 Dn when n Is Odd -- 7.5.4 Dn when n Is Even -- 7.5.5 D∞ and A(D∞) -- 7.5.6 Q8 -- 7.6 Additive Structure -- 7.6.1 M(N) -- 7.6.2 Centraliser Near-Rings -- 7.6.3 A Duality of Semi-Groups -- 7.6.4 Density -- 7.7 MS() when S Is Fixed-Point-Free -- 7.7.1 The Structure of Minimal Left Ideals -- 7.7.2 Right Near-Ring Groups -- 7.7.3 Annihilators -- 7.7.4 Chains of Left Ideals -- 7.7.5 Simple Near-Rings -- 7.7.6 Left Ideals -- 7.7.7 Modular Left Ideals -- 8 Generalisations and Sub-near-Rings of Transformation Near-Rings -- 8.1 Commutators -- 8.2 More Sub-near-Rings -- 8.2.1 Special Cases -- 8.3 Hadamard Products -- 8.4 Endomorphism Near-Rings -- 8.4.1 Related Sub-near-Rings -- 8.4.2 Sequences of Endomorphism Near-Rings -- 8.5 Other Kinds of Endomorphism Near-Ring -- 8.6 Change of Groups -- 8.6.1 Near-Loops -- 8.6.2 Homomorphisms and Normal Sub-Loops -- 8.6.3 The Host Problem -- 8.6.4 Transformations on Near-Loops -- 8.6.5 Transformations on Sets -- 8.7 The Stemhome Near-Ring -- 8.7.1 The Stemhome Functor -- 8.8 The Wurzel -- 8.9 Elementary Closure Procedures -- 8.9.1 Additive and Multiplicative Closures -- 8.9.2 A Topological Closure -- 8.10 Polynomials -- 8.10.1 Near-Rings -- 8.10.2 Skew Polynomial Near-Rings -- 9 Phomomorphisms -- 9.1 General Theory -- 9.1.1 Extending Mappings to Phomomorphisms -- 9.1.2 Phomomorphism-Invariant Subgroups -- 9.2 Cohomology Groups. 9.2.1 Non-abelian Group Cohomology. |
| Record Nr. | UNISA-996466556303316 |
|
Lockhart Robert (Mathematician)
|
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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