Some remarks on almost projective envelopes

Let R be a commutative ring. An R-module M is said to be almost projective if Ext¹R(M, N) = 0 for any Rₘ-module N and any maximal ideal m of R. In this paper, we investigate rings R over which every R-module has an almost projective envelope. We also characterize rings R over which every R-module has an almost projective envelope with some special properties.