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Classically semisimple rings : a perspective through modules and categories / / Martin Mathieu
Classically semisimple rings : a perspective through modules and categories / / Martin Mathieu
Autore Mathieu Martin
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (159 pages)
Disciplina 512.4
Soggetto topico Anells (Àlgebra)
Soggetto genere / forma Llibres electrònics
ISBN 9783031142093
9783031142086
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Introduction -- 1 Motivation from Ring Theory -- 1.1 Basics on Modules -- 1.1.1 Reducing Complicated Rings to Simpler Ones -- 1.1.2 One-Sided Ideals in Noncommutative Rings -- 1.1.3 Images of Ideals Under Homomorphisms -- 1.1.4 Embedding into the Endomorphism Ring and General Representations -- 1.1.5 Group Representations -- 1.2 Categories of Modules -- 1.3 Exercises -- 2 Constructions with Modules -- 2.1 Some Special Morphisms -- 2.2 Quotient Modules -- 2.3 Generating Modules -- 2.4 Direct Sums and Products of Modules -- 2.5 Free Modules -- 2.6 Special Objects in a Category -- 2.6.1 Free Objects -- 2.6.2 Products and Coproducts -- 2.7 Exercises -- 3 The Isomorphism Theorems -- 3.1 Isomorphisms Between Modules -- 3.2 Functors and Natural Transformations -- 3.3 Exercises -- 4 Noetherian Modules -- 4.1 Permanence Properties of Noetherian Modules -- 4.2 Exact Categories and Exact Functors -- 4.2.1 Kernels and Cokernels -- 4.2.2 Exact Categories -- 4.2.3 Exact Functors -- 4.3 Exercises -- 5 Artinian Modules -- 5.1 Finitely Cogenerated Modules -- 5.2 Commutative Artinian Rings -- 5.3 Artinian vs. Noetherian Modules -- 5.4 Abelian Categories -- 5.5 Exercises -- 6 Simple and Semisimple Modules -- 6.1 Decomposition of Modules -- 6.2 Projective and Injective Modules -- 6.3 Projective and Injective Objects -- 6.4 Exercises -- 7 The Artin-Wedderburn Theorem -- 7.1 The Structure of Semisimple Rings -- 7.2 Maschke's Theorem -- 7.3 The Hopkins-Levitzki Theorem -- 7.4 Exercises -- 8 Tensor Products of Modules -- 8.1 Tensor Product of Modules -- 8.2 Tensor Product of Algebras -- 8.3 Adjoint Functors -- 8.4 Exercises -- 9 Exchange Modules and Exchange Rings -- 9.1 Basic Properties of Exchange Modules -- 9.2 Exchange Rings -- 9.3 Commutative Exchange Rings -- 9.4 Exercises -- 10 Semiprimitivity of Group Rings.
10.1 Basic Properties -- 10.2 Some Analytic Structure on ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (double struck upper C left bracket upper G right bracket) /StPNE pdfmark [/StBMC pdfmarkC[G]ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 10.3 The Semiprimitivity Problem -- 10.4 Exercises -- Bibliography -- Index of Symbols -- Index.
Record Nr. UNISA-996503549603316
Mathieu Martin  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Classically Semisimple Rings : A Perspective Through Modules and Categories / / by Martin Mathieu
Classically Semisimple Rings : A Perspective Through Modules and Categories / / by Martin Mathieu
Autore Mathieu Martin
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (159 pages)
Disciplina 512.4
Collana Mathematics and Statistics Series
Soggetto topico Mathematics
Algebra
Commutative algebra
Commutative rings
Algebra, Homological
Commutative Rings and Algebras
Category Theory, Homological Algebra
ISBN 9783031142093
9783031142086
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- Chapter 1. Motivation from Ring Theory -- Chapter 2. Constructions with Modules -- Chapter 3. The Isomorphism Theorems -- Chapter 4. Noetherian Modules -- Chapter 5. Artinian Modules -- Chapter 6. Simple and Semisimple Modules -- Chapter 7. The Artin-Weddeburn Theorem -- Chapter 8. Tensor Products of Modules -- Chapter 9. Exchange Modules and Exchange Rings -- Chapter 10. Semiprimitivity of Group Rings -- Bibliography -- Index of Symbols -- Index. .
Record Nr. UNINA-9910637742003321
Mathieu Martin  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui