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A note on $S$-coherent rings
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abstract
In this note, we show that a ring $R$ is $S$-coherent if and only if every finitely presented $R$-module is $S$-coherent, providing a positive answer to a question proposed in [D. Bennis, M. El Hajoui, {\it On $S$-coherence}, J. Korean Math. Soc. \textbf{55} (2018), no.6, 1499-1512]. Besides, we show that $c$-$S$-coherent rings are $S$-coherent, and give an example to show the converse is not true in general.
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Cited by 1 Pith paper
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Some new module-theoretic characterizations of $S$-coherent rings
S-coherent rings are characterized via s-absolutely pure modules, s-pure quotients, and s-flatness of products of flat modules.
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