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Gr\"obner-Shirshov bases for Rota-Baxter algebras.

Tue, 08/18/2009 - 11:53 — SomNambul
Authors: L.A. Bokut, Yuqun Chen, Xueming Deng
Subjects: Rings and Algebras
link: http://arxiv.org/abs/0908.2281
Abstract

In this paper, we establish the Composition-Diamond lemma for associative
nonunitary Rota-Baxter algebras with weight $\lambda$. As applications, we
obtain a linear basis of a free commutative Rota-Baxter algebra without unity,
show that every countably generated Rota-Baxter algebra with weight 0 can be
embedded into a two-generated Rota-Baxter algebra and prove the 1/2-PBW
Theorems for dendriform dialgebra and trialgebra.

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