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

Abstract

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