t-Dual Baer Modules and t-Lifting Modules

We introduce the notions of t-lifting modules and t-dual Baer modules, which are generalizations of lifting modules. It is shown that an amply supplemented module M is t-lifting if and only if M is t-dual Baer and a t-K-module. We also prove that, over a right perfect ring R, every noncosingular right R-module is injective if and only if every right R-module is t-dual Baer if and only if every right R-module is t-lifting if and only if every injective right R-module is t-lifting.