由正则理想确定的凝聚性研究

The Coherence Study Determined by Regular Ideals

设R是交换环,M是R-模,T表示R的有限生成正则理想的集合.引入正则平坦模和正则余平坦模的概念,并利用正则平坦模和正则余平坦模刻画正则凝聚环,证明正则凝聚环刻画的Chase定理.特别地,证明Prüfer环是一类典型的正则凝聚环,证明R是Prüfer环当且仅当可除模是正则余平坦模,当且仅当正则余平坦模的商模是正则余平坦模.

Let R be a commutative ring, M be a R-module and T be a set of finitely generated regular ideals of R. In this paper we introduce the concepts of regular flat modules and regular coflat modules, and characterize regular coherent rings by using regular coflat modules and regular flat modules. It is proved that the famous Chase’s theorem on regular coherent rings. In particular, it is shown that Prüfer rings are typical regular coherent rings. And it is proved that R is a Prüfer ring if and only if all divisible modules are regular coflat modules;if and only if factor modules of regular coflat modules are regular coflat modules.