Localization of Rota-Baxter algebras

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• 作者：Chenghao Chu ; Li Guo
• 关键词：13B30 ; 13F99 ; 16W99
• 刊名：Journal of Pure and Applied Algebra
• 出版年：February, 2014
• 年：2014
• 卷：218
• 期：2
• 页码：237-251
• 全文大小：454 K

文摘

A commutative Rota-Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota-Baxter algebras, we extend the central concept of localization for commutative algebras to commutative Rota-Baxter algebras. The existence of such a localization is proved and, under mild conditions, its explicit construction is obtained. The existence of tensor products of commutative Rota-Baxter algebras is also proved and the compatibility of localization and the tensor product of Rota-Baxter algebras is established. We further study Rota-Baxter coverings and show that they form a Grothendieck topology.