Free Ideal Rings and Localization in General Rings Hardback
by P. M. (University College London) Cohn
Part of the New Mathematical Monographs series
Hardback
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.
Information
-
Out of stock
- Format:Hardback
- Pages:594 pages, Worked examples or Exercises; 38 Line drawings, unspecified
- Publisher:Cambridge University Press
- Publication Date:08/06/2006
- Category:
- ISBN:9780521853378
Information
-
Out of stock
- Format:Hardback
- Pages:594 pages, Worked examples or Exercises; 38 Line drawings, unspecified
- Publisher:Cambridge University Press
- Publication Date:08/06/2006
- Category:
- ISBN:9780521853378
