Prüfer整环是交换环理论中一种重要的环类,它在代数数论、同调代数和乘法理想理论等的研究中起着重要的作用.主要研究了Prüfer整环的一种推广—几乎Prüfer整环的性质,给出了如下2个结果:几乎赋值整环的反向极限是几乎赋值整环;几乎Prüfer整环的反向极限在riding假设的条件下是几乎Prüfer整环.但在一般条件下,给出例子说明几乎Prüfer整环的反向极限未必是几乎Prüfer整环。
Prüfer domain is an important class of rings in commutative ring theory.It plays a basic role in algebraic number theory,homological algebra theory and multiplicative ideal theory.In this paper,the properties of almost Prüfer domains extended from Prüfer domains are studied.The following two results are proved.The inverse limit of almost valuated domain is an almost valuated domain.The inverse limit of almost Prüfer domain is an almost Pr üfer domain under the riding assumption.In general cases,an example of the inverse limit of an almost Pr üfer domain is given that is not an almost Prüfer domain.