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arXiv · 2411.14142

Some new module-theoretic characterizations of $S$-coherent rings

Xiaolei Zhang
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Abstract

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then, we give some new characterizations of $S$-coherent rings in terms of $s$-absolutely pure modules.

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Xiaolei Zhang. 2024-11-21. Some new module-theoretic characterizations of $S$-coherent rings. https://arxiv.org/abs/2411.14142

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