Composition-Diamond Lemma for Tensor Product of Free Algebras

L. A. Bokut; Yuqun Chen; Yongshan Chen

doi:10.1016/j.jalgebra.2010.02.021

Composition-Diamond Lemma for Tensor Product of Free Algebras

Rings and Algebras 2010-04-21 v2

Authors: L. A. Bokut , Yuqun Chen , Yongshan Chen

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

Composition-Diamond lemma Tensor product Free algebras Groebner-Shirshov basis Commutative algebra Noncommutative algebra Lifting basis

Cite

@article{arxiv.0804.2115,
  title  = {Composition-Diamond Lemma for Tensor Product of Free Algebras},
  author = {L. A. Bokut and Yuqun Chen and Yongshan Chen},
  journal= {arXiv preprint arXiv:0804.2115},
  year   = {2010}
}

Comments

19 pages

Related papers

View all related →