Cofinitely Rationally Closed Weak Supplemented Modules

The module is cofinitely rationally closed weak supplemented module (denoted by CRCWS-module) if every cofinite rationally closed submodule of has weak supplement submodule in . The CRCWS- module is stronger generalize of closed cofinitely weak supplemented modules. In addition, we present a rationally closed weak supplemented modules (denoted by RCWS-module) which is a stronger generalize of closed weak supplemented modules. The relationships of our concepts to other related concepts was discussed and studied, and we give the conditions that make them equivalent were given. And also, we gave the necessary condition that makes the direct sum of RCWS-module (or CRCWS-module) is RCWS-module (CRCWS-module).