| Dewey Class |
518 |
| Titolo |
Algorithmic Methods in Non-Commutative Algebra ([EBook] :) : Applications to Quantum Groups / / by José Bueso, José Gómez-Torrecillas, Alain Verschoren. |
| Autore |
Bueso, José |
| Added Personal Name |
Gómez-Torrecillas, José author. |
| Verschoren, Alain author. |
| Other name(s) |
SpringerLink (Online service) |
| Pubblicazione |
Dordrecht : : Springer Netherlands : : Imprint: Springer, , 2003. |
| Physical Details |
XI, 300 p. : online resource. |
| Serie |
Mathematical modelling : theory and applications 1386-2960 ; ; 17 |
| ISBN |
9789401702850 |
| Summary Note |
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.: |
| Contents note |
1. 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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-94-017-0285-0 |
| Link alle Opere Legate |
Riferimenti soggetto: .
Algebraic Geometry .
Algorithms .
Associative rings .
Associative Rings and Algebras .
Category Theory, Homological Algebra .
Category theory (Mathematics) .
Computer Science .
Homological algebra .
Numeric Computing .
Numerical Analysis .
Rings (Algebra) .
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