Composition-Diamond Lemma for Tensor Product of Free Algebras
arXiv:0804.2115 · doi:10.1016/j.jalgebra.2010.02.021
Abstract
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.
19 pages