Z*-SMALL SUBMODULES AND Z*-HOLLOW MODULES

This work introduces a new class of submodules which we call Z*-small, Z*-maximal and Z*-radical submodules. We show that there is no general relation between the maximal and Z*-maximal submodules. In contrast, Z*-small and Z*-radical submodules are generalizations of the small and radical submodules. Also, this work introduces a new class of modules called Z*-hollow and Z*-semihollow as a generalization of the hollow and semihollow modules and shows no general relation between e*-essential small and Z*-small. Further, this work studies some properties of those concepts, such as the finite sums, direct sums and images of those concepts. Finally, this work investigates submodules which are not Z*-small, Z*-maximal, Z*-radical, Z*-hollow, or Z*-semihollow.