4th International Conference on Pure and Applied Mathematics, Van, Turkey, 22 - 23 June 2022, pp.146
Throughout this talk, all rings considered are associative with an identity element and all modules at hand are right and unital.
It is shown that over an arbitrary ring the class of all short exact sequences such that Im is a wsa-supplement in N is a proper class. We study the objects of this class, which we call WSS. We show that a module M is WSS-coinjective if and only if it is a wsa-supplement E(M). We prove that over a right CC-ring a projective module P is WSS-coinjective if and only if P= wsa(P) is injective. We also prove that a ring R is weakly semiartinian if and only if every right R-module is WSS-coinjective. Finally, we show that over a crumbling-free ring
WSS-coprojective modules are only the projective modules.