A Research on the Generalizations of Modules Whose Submodules are Isomorphic to a Direct Summand

Authors : Fatih Karabacak, Özgür Taşdemir

Pages : 268-278

Doi:10.18185/erzifbed.1371910

View : 60 | Download : 62

Publication Date : 2024-03-28

Article Type : Research Paper

Abstract :A module M is called virtually semisimple (resp. virtually extending) if every submodule (resp. complement submodule) of M is isomorphic to a direct summand of M. It is known that virtually extending modules is a generalization of virtually semisimple modules. In this paper, the relationships between virtually extending modules and other generalizations of virtually semisimple modules are examined. Moreover, we introduce a new generalization of virtually semisimple modules; namely CH modules: We say a module M is a c-epi-retractable (or briefly CH module) if any complement submodule of M is a homomorphic image of M. CH modules contains the class of virtually extending modules and the class of epi-retractable modules. We also give some basic properties of this new module class.
Keywords : virtually extending module, epi retractable module, CH module, virtually semisimple module