Free Ideal Rings and Localization in General Rings (Hardcover)

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	New Mathematical Monographs
Release date:	June 2006
First published:	2006
Authors:	P. M. Cohn
Dimensions:	234 x 160 x 34mm (L x W x T)
Format:	Hardcover
Pages:	594
ISBN-13:	978-0-521-85337-8
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	0-521-85337-0
Barcode:	9780521853378

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