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Gröbner bases in ring theory /
This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a qu...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi- )primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non- )homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations). |
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| Descripción Física: | 1 online resource (x, 284 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 271-280) and index. |
| ISBN: | 9789814365147 9814365149 1299671837 9781299671836 |