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Idempotent analysis / V. P. Maslov, Samborskii, editors
| Idempotent analysis / V. P. Maslov, Samborskii, editors |
| Autore | Maslov, V. P. |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, c1992 |
| Descrizione fisica | xi, 210 p. ; 26 cm. |
| Disciplina | 515.7 |
| Altri autori (Persone) | Samborskii, S. N. |
| Collana | Advances in soviet mathematics, ISSN 10518037 ; 13 |
| Soggetto topico |
Asymptotic behavior of solutions
Near-rings Semigroups of transformations Semirings |
| ISBN | 0821841149 |
| Classificazione |
AMS 16Y
AMS 16Y30 AMS 16Y60 AMS 20M20 AMS 35B40 AMS 35F20 AMS 47B38 AMS 49L05 AMS 49L20 AMS 49L99 AMS 90C27 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000989749707536 |
Maslov, V. P.
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| Providence, R. I. : American Mathematical Society, c1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Near-rings : the theory and its applications / Gunter Pilz
| Near-rings : the theory and its applications / Gunter Pilz |
| Autore | Pilz, Gunter |
| Pubbl/distr/stampa | Amsterdam : North-Holland, 1977 |
| Descrizione fisica | xiv, 393 p. ; 24 cm |
| Disciplina | 512.4 |
| Collana | North-Holland mathematics studies, 0304-0208 ; 23 |
| Soggetto topico | Near-rings |
| ISBN | 0720405661 |
| Classificazione |
AMS 16-02
AMS 16-XX AMS 16Y30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001164259707536 |
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Pilz, Gunter
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| Amsterdam : North-Holland, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Near-rings and their links with groups / J. D. P. Meldrum
| Near-rings and their links with groups / J. D. P. Meldrum |
| Autore | Meldrum, J. D. P. |
| Pubbl/distr/stampa | Boston ; Somerset, N.J. : Pitman Advanced Publ. Program, 1985 |
| Descrizione fisica | 275 p. ; 25 cm. |
| Disciplina | 512.4 |
| Collana | Pitman research notes in mathematics series, ISSN 02693674 ; 134 |
| Soggetto topico |
Group theory
Near-rings Semigroups |
| ISBN | 0273087010 |
| Classificazione |
AMS 16A76 (1985)
AMS 20E99 AMS 20M99 QA251.5.M45 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001164329707536 |
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Meldrum, J. D. P.
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| Boston ; Somerset, N.J. : Pitman Advanced Publ. Program, 1985 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Nearrings : some developments linked to semigroups and groups / by Celestina Cotti Ferrero and Giovanni Ferrero
| Nearrings : some developments linked to semigroups and groups / by Celestina Cotti Ferrero and Giovanni Ferrero |
| Autore | Cotti Ferrero, Celestina |
| Pubbl/distr/stampa | Dordrecht ; Boston ; London : Kluwer Academic Publishers, c2002 |
| Descrizione fisica | xvii, 609 p. ; 25 cm |
| Disciplina | 512.4 |
| Altri autori (Persone) | Ferrero, Giovanni |
| Collana | Advances in mathematics ; 4 |
| Soggetto topico | Near-rings |
| ISBN | 1402008759 |
| Classificazione |
AMS 16Y30
LC QA251.5.C68 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000502159707536 |
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Cotti Ferrero, Celestina
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| Dordrecht ; Boston ; London : Kluwer Academic Publishers, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Nearrings, nearfields and related topics / / editors, Kuncham Syam Prasad [and nine others]
| Nearrings, nearfields and related topics / / editors, Kuncham Syam Prasad [and nine others] |
| Pubbl/distr/stampa | Singapore : , : World Scientific, , 2017 |
| Descrizione fisica | 1 online resource (324 pages) : illustrations, photographs |
| Disciplina | 512/.46 |
| Soggetto topico |
Near-rings
Associative rings Near-fields Algebraic fields |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910155541803321 |
| Singapore : , : World Scientific, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Proceedings of conference on near-rings and near-fields[ : San Benedetto del Tronto 13/19 settembre 1981] / edited by G. Ferrero e C. Ferrero Cotti ; with the cooperation of G. Betsch ... [et al.] ; sponsored by Univ. Parma, CNR, Amm. Com. S. Benedetto del Tronto, Azienda Aut. Sogg. S. Benedetto del Tronto
| Proceedings of conference on near-rings and near-fields[ : San Benedetto del Tronto 13/19 settembre 1981] / edited by G. Ferrero e C. Ferrero Cotti ; with the cooperation of G. Betsch ... [et al.] ; sponsored by Univ. Parma, CNR, Amm. Com. S. Benedetto del Tronto, Azienda Aut. Sogg. S. Benedetto del Tronto |
| Autore | Ferrero Cotti, C. |
| Pubbl/distr/stampa | [S.l.] : Tecnografica, 1982 |
| Descrizione fisica | vii, 224 p. ; 24 cm. |
| Disciplina | 512.4 |
| Altri autori (Persone) | Ferrero, Giovanni |
| Soggetto topico | Near-rings |
| Classificazione |
AMS 12K05
AMS 16Y30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001260209707536 |
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Ferrero Cotti, C.
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| [S.l.] : Tecnografica, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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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 |
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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 |
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Lockhart Robert (Mathematician)
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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