A well known problem in the theory of envelopes is to characterize those rings having the property that every (finitely generated, finitely presented, simple) module has a projective (pre)envelope. In this paper, we introduce the [Formula: see text]-projective modules for an arbitrary class [Formula: see text] of finitely generated modules, and characterize in this general setting those rings for which every module in [Formula: see text] has a projective preenvelope.
