Composition-Diamond Lemma for Tensor Product of Free Algebras

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

References in corpus (2)

• Groebner-Shirshov bases for dialgebras
• Groebner-Shirshov Bases: Some New Results

Cited by in corpus (11)

• Gröbner-Shirshov bases and their calculation
• Gröbner-Shirshov bases for Lie algebras over a commutative algebra
• Gröbner-Shirshov bases for semirings
• Composition-Diamond lemma for differential algebras
• Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases
• Gröbner-Shirshov bases for some Lie algebras
• Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra
• Gröbner-Shirshov bases and PBW theorems
• Infinitely dimensional, affine nil algebras $A\otimes A^{op}$ and $A\otimes A$ exist
• Gröbner-Shirshov bases for categories
• Averaging algebras, rewriting systems and Gr$\ddot{o}$bner-Shirshov bases