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Free Ideal Rings and Localization in General Rings
Hardback
Main Details
| Title |
Free Ideal Rings and Localization in General Rings
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| Authors and Contributors |
By (author) P. M. Cohn
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| Series | New Mathematical Monographs |
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| Physical Properties |
| Format:Hardback | | Pages:594 | | Dimensions(mm): Height 234,Width 160 |
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| Category/Genre | Algebra |
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| ISBN/Barcode |
9780521853378
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| Classifications | Dewey:512.4 |
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| Audience | | Professional & Vocational | |
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| Illustrations |
Worked examples or Exercises; 38 Line drawings, unspecified
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Publishing Details |
| Publisher |
Cambridge University Press
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| Imprint |
Cambridge University Press
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| Publication Date |
8 June 2006 |
| Publication Country |
United Kingdom
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Description
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.
Author Biography
Paul Cohn is a Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London.
Reviews'This book presents the theory of free ideal rings (firs) in detail.' L'enseignement mathematique
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