THEORY OF CLEAN RINGS AND MATRICES

This is the first monograph devoted to clean ring and matrix theory. It aims to study a theory of expressing an element in a ring as the sum of some special ones, such as idempotents, units, nilpotents, tripotents, involutions, etc. A matrix over such rings is thereby expressed as the sum of some special matrices. Also another topics on the behaviors of topological properties and *-properties of such rings are investigated.

The book is based on the results of various published papers, particularly, by the authors'. It is accessible for students familiar with general abstract algebra, while the topics are interesting for researchers in the field of ring, matrix and operator theory.

Contents:

• Strongly Clean Conditions
• Matrices over Commutative Rings
• Triangular and Generalized Matrix Rings
• Strong J-Cleanness
• Strong Nil-cleanness
• Classes of Strongly Clean Rings
• Clean Properties
• Rings Generated by Certain Elements
• Weakly Clean and Weakly Nil-clean Properties
• Periodic and Weakly Periodic Rings
• Conditions on Zero-divisors
• Topological Structures
• Rings of Continuous Functions
• Rings with Involutions
• The Generalized Drazin Inverse

Readership: Graduate students and researchers in algebra and analysis, especially, ring and matrix theory, operator theory. Researchers in applied and computation related to generalized inverse.

Key Features:

• This is the first book giving an extensive research on clean rings and matrices. It includes almost all known results in the last decade
• As it is self-contained, readers are easy to read with general abstract algebra and get a systemic knowledge on such topics in a short time