Composition–Diamond lemma for tensor product of free algebras

• DOI: 10.1016/j.jalgebra.2010.02.021
• Publication Date: 2010-03-12T12:52:47Z
• Authors: L.A. Bokut; Yuqun Chen; Yongshan Chen
• Keywords: Lemma (botany); Basis (linear algebra)

19 pages<br/>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.<br/>