Resumen de Localization of Rota�Baxter algebras

Chenghao Chu, Li Guo

• 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.

  Wefurther study Rota�Baxter coverings and show that they form a Grothendieck topology.