On generalizations of semiperfect and perfect rings

We call a ring R right generalized semiperfect if every simple right R-module is an epimorphic image of a flat right R-module with small kernel, that is, every simple right R-module has a flat B-cover. We give some properties of such rings along with examples. We introduce flat strong covers as flat covers which are also aflat B-covers and give characterizations of A-perfect, B-perfect and perfect rings in terms of flat strong covers.