Some remarks on almost projective envelopes

Xiaolei Zhang, Wei Qi, Dechuan Zhou

Let $R$ be a commutative ring. An $R$-module $M$ is said to be almost projective if ${\mathrm{Ext}}_R^1(M,N)=0$ for any $R_{\mathfrak{m}}$-module $N$ and any maximal ideal $\mathfrak…