Groebner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras

Details Groebner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras Groebner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras

2008-05-06

arxiv.org/abs/0805.0640v2

Journal of Pure and Applied Algebra, 214(2010), 89-100.

Mathematics

Rings and Algebras

21 pages

Scientific paper

In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Groebner-Shirshov bases of free Rota-Baxter algebra, $\lambda$-differential algebra and $\lambda$-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar to those obtained by Ebrahimi-Fard and Guo, and Guo and Keigher recently by using other methods.

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