上有限I-补模

摘要

设R是环,M是环R上的左模,I是R的理想.称M为上有限I-补模,若对于M的任意上有限子模X,存在M的子模y,使得X+Y=M,X∩Yc(∈)IY且X∩Y在Y中是PSD的.该定义推广了I-补模.并给出了上有限I-补模的一些性质.%Let R be a ring,M be a left module over a ring R and I an ideal of R. A module M is called cofi-nitely I-supplemented if for every cofinite submodule X of Y, there is a submodule Y of M such that X+ Y=M,X∩Y(C)IYand X∩Y is PSD in Y. This definition generalizes I-supplemented modules. Some properties of cofinitely I-supplemented modules are given.