H^*-condition on the set of submodules of a module

In this work, we introduce H^*-condition on the set of submodules of a module. Let M be a module. We say M satisfies H^* provided that for every submodule N of M, there is a direct summandD of M such that (N+D)/N and (N+D)/D are cosingular. We show that over a right perfect right GV-ring,a homomorphic image of a H^* duo module satisfies H^*.

Keywords:

H-supplemented module , cosingular module , H^*-module