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Let R be a commutative ring. An R-module M is said to be almost projective if Ext¹R (M, N) = 0 for any R₌-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.
Zhang et al. (Tue,) studied this question.