Quasi-Dual Modules.

Let R be a ring, M be a right R-module and S = EndR(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of rM(X) where X ⊆ S. In this article, we study and provide several characterizations of this module classes. We show that if M is quasi-dual module, then, for all m ∈ M, rMlS(m) = mR ⊕ K for some submodule K of M. We also show that every quasidual module is a Kasch module and Z(SM) ⊆ Rad(MR). [ABSTRACT FROM AUTHOR]