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Cambridge University Press Free Ideal Rings and Localization in General Rings: 3 (New Mathematical Monographs, Series Number 3)

Name: Free Ideal Rings and Localization in General Rings: 3 (New Mathematical Monographs, Series Number 3)
Brand: Cambridge University Press

9780521853378

Algebra

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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.

Product Specifications

Brand: Cambridge University Press
Model: 9780521853378
Format: hardcover
ASIN: 0521853370
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 08 June 2006
Listed Since: 27 December 2006

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Cambridge University Press Free Ideal Rings and Localization in General Rings: 3 (New Mathematical Monographs, Series Number 3)

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