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...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press
2006.
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| Colección: | CUP ebooks.
New mathematical monographs ; 3. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b45432259*spi |
| Sumario: | 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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| Descripción Física: | 1 recurso electrónico (xxii, 572 páginas) |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9780511542794 |
