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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.
Sample Chapter(s)
Chapter 1: Stable Range One (333 KB)
Contents:
- 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
Readership: Mathematicians and graduate students interested in ring and module theory.
