S-coherent rings are characterized via s-absolutely pure modules, s-pure quotients, and s-flatness of products of flat modules.
On uniformly $S$-coherent rings
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abstract
In this paper, we introduce and study the notions of uniformly $S$-finitely presented modules and uniformly $S$-coherent rings (modules) which are "uniform" versions of ($c$-)$S$-finitely presented modules and ($c$-)$S$-coherent rings (modules) introduced by Bennis and Hajoui \cite{bh18}. Among the results, uniformly $S$-versions of Chase's result, Chase Theorem and Matlis Theorem are obtained.
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math.AC 1years
2024 1verdicts
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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.