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arXiv · 2406.02005

Some remarks on almost projective envelopes

Xiaolei Zhang·Wei Qi·Dechuan Zhou
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Abstract

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

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Xiaolei Zhang, Wei Qi, Dechuan Zhou. 2024-06-04. Some remarks on almost projective envelopes. https://arxiv.org/abs/2406.02005

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