Let R be a ring, M be a right R-module and S = End_R(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of r_M(X) where X \subseteq 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 \in M, r_M \ell_S(m) = mR \oplus K for some submodule K of M. We also show that every quasi-dual module is a Kasch module and Z(_SM) \subseteq Rad (M_R).
Quasi-dual module, Kasch module, Ikeda-Nakayama module
KOŞAN, M. TAMER (2006) "Quasi-Dual Modules," Turkish Journal of Mathematics: Vol. 30: No. 2, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol30/iss2/4