GENERALIZED COFINITELY delta-SEMIPERFECT MODULES

Abstract

Let R be a ring and M be a left R-module. M is called a cofinitely generalized (weak) delta-supplemented module or briefly a delta-CGS-module (delta-CGWS-module) if every cofinite submodule of M has a generalized (weak) delta-supplement in M. In this paper, we give various properties of these modules. It is shown that (1) The class of cofinitely generalized (weak) delta-supplemented modules are closed under taking homomorphic images, arbitrary sums, generalized delta-covers and closed under extensions. (2) M is a generalized cofinitely delta-semiperfect module if and only if M is a cofinitely generalized delta-supplemented by generalized delta-supplements which have generalized projective delta-covers.