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On uniformly $S$-coherent rings

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arxiv 2205.07137 v3 pith:HGPXPI3Y submitted 2022-05-14 math.AC

Xiaolei Zhang This is my paper · ORCID
classification math.AC
keywords modulesuniformlycoherentringschasefinitelypresentedtheorem
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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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  1. Some new module-theoretic characterizations of $S$-coherent rings

    math.AC 2024-11 conditional novelty 4.0 of 10

    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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