References & Citations
Mathematics > Commutative Algebra
Title: A note on $S$-coherent rings
(Submitted on 12 May 2024 (v1), last revised 19 May 2024 (this version, v2))
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.
Submission history
From: Xiaolei Zhang [view email][v1] Sun, 12 May 2024 12:36:04 GMT (5kb)
[v2] Sun, 19 May 2024 02:56:31 GMT (7kb)
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