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

الأصل · EN

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.