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OverviewThe 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. Full Product DetailsAuthor: J.L. Bueso , José Gómez-Torrecillas , A. VerschorenPublisher: Springer Imprint: Springer Edition: Softcover reprint of hardcover 1st ed. 2003 Volume: 17 Dimensions: Width: 15.50cm , Height: 1.60cm , Length: 23.50cm Weight: 0.486kg ISBN: 9789048163281ISBN 10: 9048163285 Pages: 300 Publication Date: 08 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1. Generalities on rings.- 2. Gröbner basis computation algorithms.- 3. Poincaré-Birkhoff-Witt Algebras.- 4. First applications.- 5. Gröbner bases for modules.- 6. Syzygies and applications.- 7. The Gelfand-Kirillov dimension and the Hilbert polynomial.- 8. Primality.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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