IC-Pseudo-Injective Modules

In this work, the notion of pseudo-injectivity relative to a class of submodules (namely, ic-pseudo-injectivity) has been introduced and studied, which is a proper generalization of pseudo-injectivity and continuity. This no- tion is closed under direct summands. Several properties and characterizations have been given. Continuous and quasi-continuous modules are characterized in terms of lifting monomorphisms of certain submodules into the module. Noetherian rings and semisimple artinian rings have been characterized in terms of ic-pseudo-injectivity.