Composition-Diamond lemma for $λ$-differential associative algebras with multiple operators

Details Composition-Diamond lemma for $λ$-differential associative algebras with multiple operators Composition-Diamond lemma for $λ$-differential associative algebras with multiple operators

2009-08-13

arxiv.org/abs/0908.1993v1

Journal of Algebra and Its Applications, Vol. 9, No. 2 (2010) 223-239

Mathematics

Rings and Algebras

Scientific paper

10.1142/S0219498810003859

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K $ with multiple operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words.

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