Some remarks on almost projective envelopes

2024/06/04 by Zhang, Xiaolei, Qi, Wei, Zhou, Dechuan
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.02005

Abstract

Let R be a commutative ring. An R-module M is said to be almost projective if \rm Ext¹_R(M, N) = 0 for any R_\mathfrakm-module N and any maximal ideal \mathfrakm 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.

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