DI—环

DI-ring

Boyle·A·K在文献[4]中分别研究了QI—环(假如每个quas(?)-injective R—模都是内射模)和V—环(假如每个单纯R—模都是内射模).本文定义并研究了DI—环,即:假如每个可除R—环都是内射模.得到: (1) 可换环R是DI—环的充要条件是R为HN—环(Hereditary Noether—环) (2) DI—环R的构造为R是阿丁环与质环的直和. (3) DI—环R的一些其它性质.

Considering the rings in which every divisible R-module is injective R-module,these rings will be referred to as DI-rings. Thus, (1) commutative ring-R is DI-ring if and only if R is Hereditary-ring and Noether-ring. (2)the structure of DI-ring is the direct sum of Artin-ring and prime ring. (3) some characters of DI-rings were given.