Ring constructions and applications / Andrei V. Kelarev.

Format:

Book

Author/Creator:

Kelarev, A. V. (Andrei V.)

Series:

Series in algebra ; v. 9.

Series in algebra ; v. 9

Language:

English

Subjects (All):

Rings (Algebra).

Physical Description:

1 online resource (218 p.)

Edition:

1st ed.

Place of Publication:

River Edge, N.J. : World Scientific, c2002.

Language Note:

English

Summary:

This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. <i>Ring Constructions and Applications</i> can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concept

Contents:

Contents ; Preface ; Chapter 1 Preliminaries ; 1.1 Groupoids ; 1.2 Groups ; 1.3 Semigroups ; 1.4 Rings ; Chapter 2 Graded Rings ; 2.1 Groupoid-Graded Rings ; 2.2 Semigroup-Graded Rings ; 2.3 Group-Graded Rings ; 2.4 Superalgebras ; Chapter 3 Examples of Ring Constructions

3.1 Direct, Subdirect and Semidirect Products3.2 Group and Semigroup Rings, Monomial Rings ; 3.3 Crossed Products ; 3.4 Polynomial and Skew Polynomial Rings ; 3.5 Skew Group and Semigroup Rings ; 3.6 Twisted Group and Semigroup Rings ; 3.7 Power and Skew Power Series Rings ; 3.8 Edge and Path Algebras

3.9 Matrix Rings and Generalized Matrix Rings 3.10 Triangular Matrix Representations ; 3.11 Morita Contexts ; 3.12 Rees Matrix Rings ; 3.13 Smash Products ; 3.14 Structural Matrix Rings ; 3.15 Incidence Algebras ; Chapter 4 The Jacobson Radical

4.1 The Jacobson Radical of Groupoid-Graded Rings 4.2 Descriptions of the Jacobson Radical ; 4.3 Semisimple Semigroup-Graded Rings ; 4.4 Homogeneous Radicals ; 4.5 Radicals and Homogeneous Components ; 4.6 Nilness and Nilpotency ; Chapter 5 Groups of Units

Chapter 6 Finiteness Conditions 6.1 Groupoid-Graded Rings ; 6.2 Structural Approach of Jespers and Okininski; 6.3 Finiteness Conditions and Homogeneous Components ; 6.4 Classical Krull Dimension and Gabriel Dimension ; Chapter 7 PI-Rings and Varieties ; Chapter 8 Gradings of Matrix Rings

8.1 Full and Upper Triangular Matrix Rings

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 157-200) and index.

ISBN:

9786611948047

9781281948045

1281948047

9789812799722

9812799729

OCLC:

879023571