Description

Book Synopsis
This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.

Table of Contents
Notational Conventions; Stable Range One; Unit 1-Stable Range; On m-Fold Stable Rings; Strongly Stable Rings; Weakly Stable Rings; Related Comparability; Generalized Stable Rings; QB-Rings; PB-Rings; Power-Cancellation; Stably Euclidean Rings; The n-Stable Range Condition; Stable Range for Ideals; Diagonal Reduction; Clean Properties, I; Clean Properties, II; Abelian Rings and Exchange.

Rings Related To Stable Range Conditions

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    A Hardback by Huanyin Chen

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      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 26/01/2011
      ISBN13: 9789814329712, 978-9814329712
      ISBN10: 9814329711

      Description

      Book Synopsis
      This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.

      Table of Contents
      Notational Conventions; Stable Range One; Unit 1-Stable Range; On m-Fold Stable Rings; Strongly Stable Rings; Weakly Stable Rings; Related Comparability; Generalized Stable Rings; QB-Rings; PB-Rings; Power-Cancellation; Stably Euclidean Rings; The n-Stable Range Condition; Stable Range for Ideals; Diagonal Reduction; Clean Properties, I; Clean Properties, II; Abelian Rings and Exchange.

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