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arXiv · 2103.14240

New Characterizations of $S$-coherent rings

Wei Qi·Xiaolei Zhang·Wei Zhao
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Abstract

In this paper, we introduce and study the class $S$-$\mathcal{F}$-ML of $S$-Mittag-Leffler modules with respect to all flat modules. We show that a ring $R$ is $S$-coherent if and only if $S$-$\mathcal{F}$-ML is closed under submodules. As an application, we obtain the $S$-version of Chase Theorem: a ring $R$ is $S$-coherent if and only if any direct product of $R$ is $S$-flat if and only if any direct product of flat $R$-modules is $S$-flat. Consequently, we provide an answer to the open question proposed by D. Bennis and M. El Hajoui [3].

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Wei Qi, Xiaolei Zhang, Wei Zhao. 2021-03-26. New Characterizations of $S$-coherent rings. https://arxiv.org/abs/2103.14240

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