Algebras, Rings and Modules, Volume 2: Non-commutative Algebras and Rings, 1st Edition (Hardback) book cover

Algebras, Rings and Modules, Volume 2

Non-commutative Algebras and Rings, 1st Edition

By Michiel Hazewinkel, Nadiya M. Gubareni

CRC Press

364 pages | 189 B/W Illus.

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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

Subject Categories

BISAC Subject Codes/Headings:
MAT002000
MATHEMATICS / Algebra / General
MAT003000
MATHEMATICS / Applied
SCI040000
SCIENCE / Mathematical Physics