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.
| ISBN: | 9780521853378 |
| Publication date: | 8th June 2006 |
| Author: | P M University College London Cohn |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 594 pages |
| Series: | New Mathematical Monographs |
| Genres: |
Algebra |
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.
Free Ideal Rings and Localization in General Rings features in the following genres: Algebra
Free Ideal Rings and Localization in General Rings is available in Hardback
Free Ideal Rings and Localization in General Rings was written by P M University College London Cohn and published by Cambridge University Press
Free Ideal Rings and Localization in General Rings has 594 pages
Yes it is part of New Mathematical Monographs series
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