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Book Cover
Author Hazewinkel, Michiel

Title Algebras, Rings and Modules, Volume 2 : Non-commutative Algebras and Rings
Published Boca Raton : CRC Press, 2017


Description 1 online resource (364 pages)
Contents Cover; Half Title; Title Page; Copyright Page; Table of Contents; Contents of Volume 2; Preface; 1: Rings Related to Finite Posets ; 1.1 Incidence Rings; 1.2 Incidence Rings I(S, D); 1.3 Right Hereditary Rings A(S, O); 1.4: Incidence Rings Modulo the Radical ; 1.5 Serial and Semidistributive Rings I(S, ĘŚ, M); 1.6 Notes and References
2: Distributive and Semidistributive Rings 2.1 Distributive Modules and Rings; 2.2 Semiprime Semidistributive Rings; 2.3 Semiperfect Semidistributive Rings; 2.4 Right Hereditary SPSD-Rings; 2.5 Semihereditary SPSD-Rings; 2.6 Notes and References; 3: The Group of Extensions ; 3.1 Module Constructions Pushout and Pullback; 3.2 The Snake Lemma
3.3 Extensions of Modules3.4 Baer Sum of Extensions; 3.5 Properties of Ext1; 3.6 Ext1 and Extensions; 3.7 Additive and Abelian Categories; 3.8 Notes and References; 4: Modules Over Semiperfect Rings ; 4.1 Finitely Generated Modules over Semiperfect Rings; 4.2 Stable Equivalence; 4.3 Auslander-Bridger Duality; 4.4 Almost Split Sequences; 4.5 Cogenerators and Some Identities for Finitely Presented Modules; 4.6 Pure Submodules and Pure Exact Sequences
4.7 Almost Split Sequences over Semiperfect Rings4.8 Linkage and Duality of Modules over Semiperfect Rings; 4.9 Notes and References; 5: Representations of Primitive Posets ; 5.1 Representations of Finite Posets; 5.2 Main Canonical Forms of Matrix Problems; 5.3 Trichotomy Lemma; 5.4 The Kleiner Lemma; 5.5 The Main Construction; 5.6 Primitive Posets of Infinite Representation Type; 5.7 Primitive Posets of Finite Representation Type; 5.8 Notes and References
6: Representations of Quivers, Species and Finite Dimensional Algebras 6.1 Finite Quivers and Their Representations; 6.2 Species, Valued Quivers and Valued Graphs; 6.3 Finite Dimensional Algebras and Their Representations; 6.4 Notes and References
Summary "The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules."--Provided by publisher
Notes 7: Artinian Rings of Finite Representation Type
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Modules (Algebra)
Rings (Algebra)
SCIENCE -- Mathematical Physics.
Modules (Algebra)
Rings (Algebra)
Form Electronic book
Author Gubareni, Nadiya M
ISBN 9781351869874