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 summand d 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∗.