Free Ideal Rings and Localization in General Rings

By Paul M. Cohn

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.

• Format: Hardcover
• Language: English
• ISBN: 0521853370
• ISBN13: 9780521853378
• Release Date: July 2006
• Publisher: Cambridge University Press
• Length: 594 Pages
• Weight: 2.10 lbs.
• Dimensions: 1.4" x 6.0" x 9.0"