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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.

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Book Details

ISBN: 9780521853378
ISBN-10: 0521853370
Format: Hardback
(228mm x 152mm x 34mm)
Pages: 594
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 8-Jun-2006
Country of Publication: United Kingdom

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Author Biography - P. M. Cohn

Paul Cohn is a Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London.

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