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Free $Ω$ $Ω$ -Rota–Baxter algebras and Gröbner–Shirshov bases

Dan Chen

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China

E-mail Address: chendan@lzu.edu.cn

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Yan-Feng Luo

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China

E-mail Address: luoyf@lzu.edu.cn

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Yi Zhang

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China

School of Mathematics and Statistics, NUIST, Nanjing, Jiangsu 210044, P. R.China

E-mail Address: zhangy2016@lzu.edu.cn

Corresponding author.

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, and

Yuan-Yuan Zhang

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China

E-mail Address: zhangyy17@lzu.edu.cn

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https://doi.org/10.1142/S0218196720500447Cited by:2 (Source: Crossref)

Abstract

Motivated by the formula of partial integration, we introduce the concept of $Ω$ $Ω$ -Rota–Baxter algebras, which generalizes the Rota–Baxter algebras introduced by Baxter. We then construct free objects in the category of $Ω$ $Ω$ -Rota–Baxter algebras, via a method of Gröbner–Shirshov bases.

Communicated by I. Shestakov

Keywords:

AMSC: 16W99, 13P10, 08B20, 17B38

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