Algorithmic Methods in Non-Commutative Algebra

J. L. Bueso

ISBN 10: 9048163285 / ISBN 13: 9789048163281

Verlag: Springer Netherlands, Springer Netherlands Dez 2010, 2010

Beschreibung

This item is printed on demand - Print on Demand Titel. Neuware -The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 316 pp. Englisch.

Bestandsnummer des Verkäufers 9789048163281

Bibliografische Details

• Titel: Algorithmic Methods in Non-Commutative Algebra
• Verlag: Springer Netherlands, Springer Netherlands Dez 2010
• Erscheinungsjahr: 2010
• Sprache: Englisch
• ISBN-10: 9048163285
• ISBN-13: 9789048163281
• Einband: Taschenbuch
• Zustand: Neu

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Inhaltsangabe

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.