Details:
Title  Composition–Diamond lemma for tensor product of free algebras  Author(s)  Leonid A. Bokut, YuFu Chen  Type  Article in Journal  Abstract  In 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.  Keywords  Gröbner–Shirshov basis, Gröbner basis, Free algebra, Polynomial algebra, Tensor product  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869310000876 
Language  English  Journal  Journal of Algebra  Volume  323  Number  9  Pages  2520  2537  Year  2010  Edition  0  Translation 
No  Refereed 
No 
