On a Variation of Co-coatomically Supplemented Modules

Abstract

Co-coatomically ss-supplemented modules are identified by extending the concept of ss-supplemented modules, and certain characteristics of co-coatomically ss-supplemented modules are demonstrated. It is established that the sum of a finite set of co-coatomically sssupplemented modules remains co-coatomically ss-supplemented. Moreover, it is proven that any quotient module of a co-coatomically ss-supplemented module is also co-coatomically sssupplemented. It is observed that if G is a co-coatomically ss-supplemented submodule of a module E with the condition that E/G lacks a maximal submodule, then E is co-coatomically ss-supplemented. It is demonstrated that the ring S is semi-perfect and (Formula Presented) if and only if S is semi-local and (Formula Presented) if and only if each left S-module is cocoatomically ss-supplemented. Furthermore, specific characteristics of co-coatomically sssupplemented modules over Dedekind rings are examined.