Free Ideal Rings and Localization in General Rings
Published on 28. August 2006
978-0-511-22306-8 (ISBN)
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.
Reviews / Votes
'This book presents the theory of free ideal rings (firs) in detail.' L'enseignement mathematiqueMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 38 Line drawings, unspecified
File size
2,96 MB
ISBN-13
978-0-511-22306-8 (9780511223068)
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Schweitzer Classification
Other editions
Additional editions
Book
06/2006
Cambridge University Press
€220.90
Shipment within 15-20 days
Person
Paul Cohn is a Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London.
Content
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.
