Free ideal rings and localization in general rings:
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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Schriftenreihe: | New mathematical monographs
3 |
| Links: | https://doi.org/10.1017/CBO9780511542794 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xxii, 572 Seiten) |
| ISBN: | 9780511542794 |
Internformat
MARC
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| 246 | 3 | |a Free Ideal Rings & Localization in General Rings | |
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| 490 | 1 | |a New mathematical monographs |v 3 | |
| 520 | |a 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. | ||
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| indexdate | 2025-03-03T11:58:04Z |
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| isbn | 9780511542794 |
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| spelling | Cohn, P. M. Free ideal rings and localization in general rings P.M. Cohn Free Ideal Rings & Localization in General Rings Cambridge Cambridge University Press 2006 1 Online-Ressource (xxii, 572 Seiten) txt c cr New mathematical monographs 3 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. Erscheint auch als Druck-Ausgabe 9780521853378 |
| spellingShingle | Cohn, P. M. Free ideal rings and localization in general rings |
| title | Free ideal rings and localization in general rings |
| title_alt | Free Ideal Rings & Localization in General Rings |
| title_auth | Free ideal rings and localization in general rings |
| title_exact_search | Free ideal rings and localization in general rings |
| title_full | Free ideal rings and localization in general rings P.M. Cohn |
| title_fullStr | Free ideal rings and localization in general rings P.M. Cohn |
| title_full_unstemmed | Free ideal rings and localization in general rings P.M. Cohn |
| title_short | Free ideal rings and localization in general rings |
| title_sort | free ideal rings and localization in general rings |
| work_keys_str_mv | AT cohnpm freeidealringsandlocalizationingeneralrings AT cohnpm freeidealringslocalizationingeneralrings |