Gr\"obner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras

Jianjun Qiu

Gr\"obner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras

Rings and Algebras 2013-01-23 v1

Authors: Jianjun Qiu

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.

Keywords

Gröbner-Shirshov bases Composition-Diamond lemma commutative algebras with multiple operators free commutative Rota-Baxter algebra free commutative λ-differential algebra Ω-words

Cite

@article{arxiv.1301.5018,
  title  = {Gr\"obner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras},
  author = {Jianjun Qiu},
  journal= {arXiv preprint arXiv:1301.5018},
  year   = {2013}
}

Comments

15pages. arXiv admin note: text overlap with arXiv:0805.0640

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