Free ideal rings and localization in general rings
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Bibliographic Information
Free ideal rings and localization in general rings
（New mathematical monographs, 3）
Cambridge University Press, 2006
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Includes bibliography and index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
by "Nielsen BookData"