Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases,International Journal of Algebra and Computation

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Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases
International Journal of Algebra and Computation ( IF 0.5 ) Pub Date : 2020-07-31 , DOI: 10.1142/s0218196720500447
Dan Chen ₁ , Yan-Feng Luo ₁ , Yi Zhang _{1,

2} , Yuan-Yuan Zhang ₁

Affiliation

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

中文翻译：

自由 Ω-Rota–Baxter 代数和 Gröbner–Shirshov 基

受偏积分公式的启发，我们引入了[公式：见正文]-Rota-Baxter代数的概念，它推广了Baxter引入的Rota-Baxter代数。然后，我们通过 Gröbner-Shirshov 基的方法在 [公式：见文本]-Rota-Baxter 代数类别中构造自由对象。

更新日期：2020-07-31

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