C-Supplemented Modules

Abstract

In this paper, we present the c-supplemented modules and give the fundamental properties of csupplemented modules. For any arbitrary ring we define a module N as c-supplemented if, for each submodule K of N, there is a submodule L in N such that N=K+L and K ∩ L is crumbling. In particular, we demonstrate that the league of c-supplemented modules exhibits closure properties under various operations, including direct sums, submodules, homomorphic images and sums. Furthermore, we confirm that for a ring S, SS is c-supplemented if every left S-module is c-supplemented.