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.
Algorithmic Methods in Non-Commutative Algebra
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basis computation algorithms, left denominator set, completely prime ideal, right greatest common divisor, ore extensions, resolvable relative, admissible order, consider the left ideal, syzygy module, monoid order, quantum plane, left noetherian, generating subspace, quantum matrices, diamond lemma, quantum relations, ner basis, left artinian, multiplicative subset, standard monomials, stable subset, overlap ambiguity, noetherian domain, classical ring, commutative case Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bergman's Diamond Lemma, Hilbert's Basis Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
basis computation algorithms, left denominator set, completely prime ideal, right greatest common divisor, ore extensions, resolvable relative, admissible order, consider the left ideal, syzygy module, monoid order, quantum plane, left noetherian, generating subspace, quantum matrices, diamond lemma, quantum relations, ner basis, left artinian, multiplicative subset, standard monomials, stable subset, overlap ambiguity, noetherian domain, classical ring, commutative case Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bergman's Diamond Lemma, Hilbert's Basis Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 23
books:
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- Graded Ring Theory (North-Holland Mathematical Library) by Constantin Nastasescu in Back Matter
- Hopf Algebras (Math Lecture Notes, No 44) by Moss E. Sweedler in Back Matter
- Introduction To Commutative Algebra by Michael Atiyah in Back Matter
- Chaos in Electronics (Mathematical Modelling: Theory and Applications) by M.A. van Wyk in Back Matter
- Advances in Decision Analysis (Mathematical Modelling: Theory and Applications) by Nadine Meskens in Back Matter
See all 23 books this book cites
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