A note on $S$-coherent rings

Fuente: arXiv
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Auteur principal: Zhang, Xiaolei
Format: Preprint
Publié: 2024
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author Zhang, Xiaolei
author_facet Zhang, Xiaolei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_07271
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A note on $S$-coherent rings
Zhang, Xiaolei
Commutative Algebra
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.
title A note on $S$-coherent rings
topic Commutative Algebra
url https://arxiv.org/abs/2405.07271