F-w-Supplemented Modules

Abstract

Let 𝑆 be a ring, let 𝐸 be a left 𝑆-module, and let 𝐻 and 𝐾 be submodules of 𝐸 where 𝐹 is proper. We call the module 𝐸 F-w-supplemented provided that each semisimple submodule of 𝐸 has an Fsupplement in 𝐸. We call the module 𝐸 amply F-w-supplemented if 𝐸 = 𝑈 + 𝑉, where 𝑈 is a semisimple submodule of 𝐸, then 𝑉 contains an F-supplement of 𝐸. In this study, we introduce F-w-supplemented modules, then we give various features of these modules.