Generalizations on z-closed submodules

In this study, the module classes which are generalizations of the CS-module class existing in the literature and specifically named as CLS, $C_{11}$, $C_{11} ^{z}$, G-extending, $G^{z}$-extending, FI-extending, PI-extending were examined in detail. Also, in $G^{z}$-extending modules, instead of $z$-closed submodules, projection invariant $z$-closed submodules were taken, and a new module class, which is a generalization of CLS and G-extending modules, was obtained. These modules, named ZPG-modules, were investigated whether their submodules, direct sums, direct summands, and injective hulls were transferred. The findings obtained through the research were compiled to contribute to the literature with the aim of guiding researchers who want to work on CS-modules and their generalizations.