FCG-内射模、FCGP-内射模与某些环

定义了左FCG－内射模和左FCGP－内射模，研究了它们的一些性质，用左FCG－内射模刻画了左V－环。称一个环R为左FCG－遗传环，如果投射左R－模的有限余生成了模是投射的。给出了环R为左FCG－遗传环的一些等价条件和左FCG－遗传环为半单环的条件。当R为左余Noether环时，R为左FCG－遗传环当且仅当R的每个有限余生成左理想是投射的。左FCG－遗传环是Morita不变的。

FCG-Injective Modules, FCGP-Injective Modules and Some Rings

Left FCG-injective modules and left FCGP-injective modules are defined, Some properties of them are investigated. Left V-rings are characlerized according to the properties of left FCG-injective modules over them. A ring R is said to be left FCG-hereditary, if each finitely cogenerated submodule of a projective left R-module is projcetive. Conditions under which a ring R to be left FCG-hereditary and conditions under which a left FCG-hereditary ring to be semisimple are given respectively. It is shown that if ring R is left co-noetherian, then it is left FCG-hereditary if and only if each finite cogenerated left ideal of it is projective. Left FCG-hereditary rings are Morita invariant.