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TitleLifting Gr\"obner bases from a class of algebras.
Author(s) Huishi Li
TypeArticle in Journal
AbstractLet K be a field, K⟨X⟩ = K⟨X 1, , X n ⟩ the free K-algebra of n generators, K Q [x i 1 , , x i n ] the multiparameter quantized coordinate ring of affine n-space with parameter matrix Q, and let π: K⟨X⟩ → K Q [x i 1 , , x i n ] be the canonical algebra epimorphism. By extending the results of [5] to K Q [x i 1 , , x i n ], we show that if G is a Gröbner basis in K Q [x i 1 , , x i n ], then a Gröbner basis 𝒢 of the pre-image ℐ = π−1(I) of the ideal I = ⟨G⟩ may be constructed subject to G (Theorem 2.3), and that the way of producing 𝒢 also simultaneously provides a criterion for the finiteness of 𝒢 (Theorem 2.6). Applications to some well-known algebras are given.
KeywordsFiltration, Gradation, Gröbner basis, Monomial ordering,
ISSN0092-7872; 1532-4125/e
URL http://www.tandfonline.com/doi/abs/10.1080/00927870903399612
LanguageEnglish
JournalCommun. Algebra
Volume38
Number6
Pages2282--2299
PublisherTaylor & Francis, Philadelphia, PA
Year2010
Edition0
Translation No
Refereed No
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