Free Ideal Rings and Localization in General Rings
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Free Ideal Rings and Localization in General Rings by P. M. Cohn
Book DescriptionProving 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 DetailsISBN: 9780521853378
(228mm x 152mm x 34mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 8-Jun-2006
Country of Publication: United Kingdom
Books By Author P. M. Cohn
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The theory of Lie groups rests on three pillars: analysis, topology and algebra.
Skew Fields, Paperback (May 2008)
This work offers a comprehensive account of skew fields and related mathematics.
Classic Algebra, Hardback (August 2000)» View all books by P. M. Cohn
Fundamental to all areas of mathematics, algebra provides the cornerstone for the student's development. The concepts are often intuitive, but some can take years of study to fully absorb. For over twenty years, the author's classic three-volume set, Algebra, has been regarded by many as the most outstanding introductory work available.
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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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