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Free Ideal Rings and Localization in General Rings.
・ISBN 978-0-521-85337-8 hard GB£ 173.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-0-511-54279-4
| 著者・編者 | Cohn, P. M., |
|---|---|
| シリーズ | New Mathematical Monographs |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2006 |
| ページ数 | 594 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-10210＞ |
解説
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.