Gabriel局部化理论及其应用
Gabriel localization theory and its applications
摘要：
本文首先发展了交换环的Gabriel局部化（简称G-局部化），特别是证明了这方面的一些新结果。作为应用，证明了环映射是平坦满射当且仅当它对应于一类G-局部化。作为研究的副产品，给出了商环平坦性的一个刻划。刻画了G-局部化函子的正合性。研究了G-局部化环中的素理想的结构。最后，证明了Gabriel局部化理论是通常局部化理论的自然推广。
英文摘要：
In this article first we develop the Gabriel localizations (abbreviated as G-localizations) for commutative rings, specially some new results in this direction are proven. Then, as an application, it is shown that a ring map is a flat epimorphism if and only if it corresponds to a kind of the G-localizations. As a by-product of this study, a characterization for the flatness of the quotient rings is given. The exactness of the G-localization functor are characterized. The structure of prime ideals in the G-localization rings are also studied. Finally, it is shown that the Gabriel localization theory is a natural generalization of the usual localization theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
