标题： 交换量化和局部化 显示英文标题

标题： Commutative Quantale and Localization

摘要： 在本文中，我们介绍了量化代数的局部化构造。 量化代数是一个完备半格与乘法结合的结构。 我们模仿格中滤子的概念，在量化代数中定义乘法滤子，并在乘法滤子处构造量化代数的局部化。 我们证明了结构类似“$\Spec R$是一个层”的定理，并利用它们在代数和几何中获得了一些结果，包括Baire范畴定理及其一些推广。 我们还提出了Baire范畴定理的一个代数版本，我们认为这在文献中尚未出现。 显示英文摘要

摘要： In this paper we introduce the localization construction for quantales. A quantale is a complete semilattice combined with a multiplication. We mimic the notion of filter in a lattice to define multiplicative filters in a quantale, and construct the localization of the quantale at a multiplicative filter. We prove theorems with similar structure as "$\Spec R$ is a sheaf" and use them to obtain several results in algebra and geometry, including the Baire Category Theorem and some of its generalizations. We also present an algebraic version of Baire Category Theorem, which we believe has not appeared in literature.