1st Edition

Algebras, Rings and Modules, Volume 2
Non-commutative Algebras and Rings




ISBN 9781138035829
Published December 12, 2016 by CRC Press
364 Pages 189 B/W Illustrations

USD $215.00

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Book Description

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.

Table of Contents

Preface

Rings Related to Finite Posets

Incidence Rings
Incidence Rings I (S; D)
Right Hereditary Rings A (S; O)
Incidence Rings Modulo the Radical
Serial and Semidistributive Rings I (S; ¤; M)
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 Ext1
Ext1 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

O-species and SPSD-rings of Bounded Representation Type
Semiperfect Rings of Bounded Representation type
O-species 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

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