Composition-Diamond Lemma for Tensor Product of Free Algebras

Details Composition-Diamond Lemma for Tensor Product of Free Algebras Composition-Diamond Lemma for Tensor Product of Free Algebras

2008-04-14

arxiv.org/abs/0804.2115v2

Journal of Algebra, 323(2010), 2520-2537.

Mathematics

Rings and Algebras

19 pages

Scientific paper

10.1016/j.jalgebra.2010.02.021

In this paper, we establish Composition-Diamond lemma for tensor product $k<
X> \otimes k< Y>$ of two free algebras over a field. As an application, we
construct a Groebner-Shirshov basis in $k< X> \otimes k< Y>$ by lifting a
Groebner-Shirshov basis in $k[X] \otimes k< Y>$, where $k[X]$ is a commutative
algebra.

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