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Algorithmic Methods in Non-Commutative Algebra
Details
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.
Inhalt
- 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.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09789048163281
- Sprache Englisch
- Auflage Softcover reprint of hardcover 1st edition 2003
- Größe H235mm x B155mm x T18mm
- Jahr 2010
- EAN 9789048163281
- Format Kartonierter Einband
- ISBN 9048163285
- Veröffentlichung 08.12.2010
- Titel Algorithmic Methods in Non-Commutative Algebra
- Autor J. L. Bueso , A. Verschoren , José Gómez-Torrecillas
- Untertitel Applications to Quantum Groups
- Gewicht 482g
- Herausgeber Springer Netherlands
- Anzahl Seiten 316
- Lesemotiv Verstehen
- Genre Mathematik