ON QUASI-DUAL BAER MODULES

We introduce and study the notions of quasi-dual Baer modules, FI-Τ -non-cosingular modules and FI-Κ-modules. We show that a module M is a quasi-dual Baer and FI-Κ-module if and only if it is FI-lifting and FI-Τ -non-cosingular. A necessary condition for a direct sum of quasi-dual Baer modules to be quasi-dual Baer are obtained. A characterization is given of when a module is quasi-dual Baer, a necessary condition being that the endomorphism ring itself is a left quasi-Baer ring.