Free Ideal Rings and Localization in General Rings
Free Ideal Rings and Localization in General Rings
$205.00
USDProving 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.
- This theory not found in any other book
- Subject is smoothly developed and well motivated
- Noncommutative theory has relations to many other topics
Reviews & endorsements
"There are handy appendices on lattice theory, category theory and homological algebra, and the ultraproduct construction. There are extensive notes to each chapter."
Mike Prest, Mathematical Reviews
Product details
August 2006Adobe eBook Reader
9780511223068
0 pages
0kg
38 b/w illus. 864 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
