Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Characterizations of $S$-coherent rings   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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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio