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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. UNINA-9910508454403321
Lockhart Robert (Mathematician)  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
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)  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui