Flat Strong δ-covers of Modules

Abstract

We say that a ring R is right generalized δ-semiperfect if every simple right R-module is an epimorphic image of a flat right R-module with δ-small kernel. This definition gives a generalization of both right δ-semiperfect rings and right generalized semiperfect rings. We provide examples involving such rings along with some of their properties. We introduce flat strong δ-cover of a module as a flat cover which is also a flat δ-cover and use flat strong δ-covers in characterizing right A-perfect rings, right B-perfect rings and right perfect rings.