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Author Hazewinkel, Michiel, author.

Title Algebras, rings, and modules : non-commutative algebras and rings. Volume 2 / Michiel Hazewinkel, Dept. of Pure and Applied Mathematics, Centrum Wiskunde & Informatica, Amsterdam, Netherlands and Nadiya Gubareni, Institute of Mathematics, Częstochowa University of Technology, Częstochowa, Poland
Published Boca Raton : CRC Press, Taylor & Francis Group, 2017
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Contents Preface -- Rings Related to Finite Posets -- Incidence Rings Incidence Rings -- Right Hereditary Rings -- Incidence Rings Modulo the Radical -- Serial and Semidistributive Rings -- Notes and References -- Distributive and Semidistributive rings -- Distributive Modules and Rings -- Semiprime Semidistributive Rings -- Semiperfect Semidistributive Rings -- Right Hereditary SPSD-rings SPSD-rings -- Notes and References -- The Group of Extensions -- Module Constructions Pushout and Pullback -- The Snake Lemma -- Extensions of Modules -- Baer Sum of Extensions -- Properties of Ext – Ext 1 and Extensions -- Additive and Abelian Categories -- Notes and References -- Modules over Semiperfect Rings -- Finitely Generated Modules over Semiperfect Rings -- Stable Equivalence -- Auslander-Bridger Duality -- Almost Split Sequences -- Cogenerators and Some Identities for Finitely Presented Modules -- Pure Submodules and Pure Exact -- Almost Split Sequences over Semiperfect Rings -- Linkage and Duality of Modules over Semiperfect Rings -- Notes and References -- Representations of Primitive Posets -- Representations of Finite Posets -- Main Canonical Forms of Matrix Problems -- Trichotomy Lemma -- The Kleiner Lemma -- The Main Construction -- Primitive Posets of Infinite Representation Type -- Primitive Posets of Finite Representation Type -- Notes and References -- Representations of Quivers, Species and Finite -- Dimensional Algebras -- Finite Quivers and Their Representations -- Species, Valued Quivers and Valued Graphs -- Finite Dimensional Algebras and Their Representations -- Notes and References -- Artinian Rings of Finite Representation Type -- Eisenbud-Griffith's Theorem -- Auslander's Theorem for Right Artinian Rings -- Artinian Semidistributive Rings -- Artinian Hereditary Semidistributive Rings of Finite -- Representation Type -- Notes and References -- (D; O)-species and SPSD-rings of Bounded Representation Type -- Semiperfect Rings of Bounded Representation type -- Ospecies and Tensor Algebras – (D; O)-species and Right Hereditary SPSD-rings -- Representations of (D; O)-species and Mixed Matrix Problems -- Some Mixed Matrix Problems -- (D; O)-species of Unbounded Representation Type -- (D; O)-species of Bounded Representation Type -- Right Hereditary SPSD-rings of Bounded Representation Type -- Notes and References -- References -- Index -- Glossary of Ring
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
Notes "A Science Publishers book."
Bibliography Includes bibliographical references and index
Subject Noncommutative algebras.
Rings (Algebra)
Noncommutative algebras.
Rings (Algebra)
Form Electronic book
Author Gubareni, Nadezhda Mikhaĭlovna, author.
ISBN 1315233045
1351869876
9781315233048
9781351869874