Free ideal rings and localization in general rings
著者
書誌事項
Free ideal rings and localization in general rings
（New mathematical monographs, 3）
Cambridge University Press, 2006
大学図書館所蔵 全23件
注記
Includes bibliography and index
内容説明・目次
内容説明
Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.
目次
- Preface
- Note to the reader
- Terminology, notations and conventions used
- List of special notation
- 0. Preliminaries on modules
- 1. Principal ideal domains
- 2. Firs, semifirs and the weak algorithm
- 3. Factorization
- 4. 2-firs with a distributive factor lattice
- 5. Modules over firs and semifirs
- 6. Centralizers and subalgebras
- 7. Skew fields of fractions
- Appendix
- Bibliography and author index
- Subject index.
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