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＜電子ブック＞
Algorithmic Methods in Non-Commutative Algebra : Applications to Quantum Groups / by J.L. Bueso, José Gómez-Torrecillas, A. Verschoren
(Mathematical Modelling: Theory and Applications ; 17)

版	1st ed. 2003.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	XI, 300 p : online resource
著者標目	*Bueso, J.L author Gómez-Torrecillas, José author Verschoren, A author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Associative rings LCSH:Associative algebras LCSH:Algorithms LCSH:Algebra, Homological LCSH:Algebraic geometry FREE:Numerical Analysis FREE:Associative Rings and Algebras FREE:Algorithms FREE:Category Theory, Homological Algebra FREE:Algebraic Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-94-017-0285-0

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