Localization of Rota�Baxter algebras

Autores: Chenghao Chu, Li Guo
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 2, 2014, págs. 237-251
Idioma: inglés
DOI: 10.1016/j.jpaa.2013.05.009
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Resumen
- 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.