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.
Produkteigenschaften
- Artikelnummer: 9789048163281
- Medium: Buch
- ISBN: 978-90-481-6328-1
- Verlag: Springer Netherlands
- Erscheinungstermin: 08.12.2010
- Sprache(n): Englisch
- Auflage: 1. Auflage. Softcover version of original hardcover Auflage 2003
- Serie: Mathematical Modelling: Theory and Applications
- Produktform: Kartoniert, Previously published in hardcover
- Gewicht: 482 g
- Seiten: 300
- Format (B x H x T): 155 x 235 x 18 mm
- Ausgabetyp: Kein, Unbekannt