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Gröbner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras (1301.5018v1)
Published 18 Jan 2013 in math.RA
Abstract: In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gr\"obner-Shirshov bases and linear bases of free commutative Rota-Baxter algebra, free commutative $\lambda$-differential algebra and free commutative $\lambda$-differential Rota-Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative $\Omega$-words.