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TitleComposition–Diamond lemma for tensor product of free algebras
Author(s) Leonid A. Bokut, Yu-Fu Chen
TypeArticle in Journal
AbstractIn this paper, we establish a Composition–Diamond lemma for the tensor product k 〈 X 〉 ⊗ k 〈 Y 〉 of two free algebras over a field. As an application, we construct a Gröbner–Shirshov basis in k 〈 X 〉 ⊗ k 〈 Y 〉 by lifting a given Gröbner–Shirshov basis in the tensor product k [ X ] ⊗ k 〈 Y 〉 in which k [ X ] is the polynomial algebra.
KeywordsGröbner–Shirshov basis, Gröbner basis, Free algebra, Polynomial algebra, Tensor product
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869310000876
LanguageEnglish
JournalJournal of Algebra
Volume323
Number9
Pages2520 - 2537
Year2010
Edition0
Translation No
Refereed No
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