Modules whose projection invariant submodules have projection invariant closures

Abstract

We elaborate the class of PC-modules in which every projection invariant submodules has projection invariant closures in this study. We provide examples that the class of PC-modules does not belong to the system of generalization of extending modules. Moreover, we clarify direct sums and direct summands properties for the former class of modules. It is proved that the aforementioned property is not closed under direct sums. Thereupon, we cope with when the direct sums of PC-modules enjoy with the property.