Abstract
In this paper we introduce the notions of tau-projective and strongly tau-projective modules relative to a preradical tau. When tau(M) = rad(M) we recover all the work that was carried out on rad-projectivity. New and interesting results are obtained in the cases where tau(M) is soc(M), Z(M) or delta(M), where soc(M), Z(M) and delta(M) denotes to the socle, the singular submodule, and the delta-submodule of M, respectively. New characterizations of semiperfect and perfect rings in terms of tau-projective covers are obtained.