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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Algebra

• Full title: Free Ideal Rings and Localization in General Rings
• Author: P. M. Cohn
• Language: English
• Binding: Hardback
• Number of pages: 594
• EAN: 9780521853378
• ISBN: 0521853370
• ID: 02047173
• Publisher: Cambridge University Press
• Weight: 961 g
• Dimensions: 234 × 160 × 34 mm
• Date of publishing: 08. June 2006

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