On S-coherence

Driss Bennis; Mohammed El Hajoui

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arXiv · 1611.05067

On S-coherence

Driss Bennis·Mohammed El Hajoui

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Abstract

Recentely, Anderson and Dumitrescu's $S$-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of $S$-finitely presented modules and then of $S$-coherent rings which are $S$-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an $S$-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other $S$-versions of finitely presented modules and coherent rings. We prove that these last $S$-versions can be characterized in terms of localization.

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Driss Bennis, Mohammed El Hajoui. 2016-11-15. On S-coherence. https://arxiv.org/abs/1611.05067

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