Co-Coatomically Ps-Supplemented Modules

In this manuscript, we introduce and study co-coatomically ps-supplemented modules. On condition that each co-coatomic submodule of an T-module A has a ps-supplement within A, then A is termed co-coatomically ps-supplemented. Each radical module is co-coatomically ps-supplemented module. On condition that each left T-module is PS-coinjective, then each left T-module is co-coatomically ps-supplemented. We show that on condition that A is semilocal and Rad(A)≪A, for A, being a cocoatomically ps-supplemented module is equivalent to being ps-supplemented. If A is co-coatomically ps-supplemented T-module, at that case the module A/(〖Soc〗_P (A) ) has each of its coatomic submodules as direct summands. Assuming T to be a left SI-ring with an essential socle, it implies that each left T-module is co-coatomically ps-supplemented.