Groebner-Shirshov Bases for Associative Algebras with Multiple Operators   and Free Rota-Baxter Algebras
  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. 
L. A. Bokut, Yuqun Chen and Jianjun Qiu