关于$S$扁平预包络的说明

arXiv - MATH - Commutative Algebra Pub Date : 2024-08-20 DOI:arxiv-2408.10523

Xiaolei Zhang

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引用次数: 0

摘要

在这篇论文中，我们研究了模块的$S$平前包络的概念。特别是，我们举例说明，环$R$是相干的并不意味着每个$R$模块都有一个$S$平前包络，从而对本尼和布兹里提出的问题给出了否定的答案。此外，我们还证明了 $R_S$ 是相干环一般也不意味着 $R$ 是 $S$ 相干环。

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A note on $S$-flat preenvelopes

In this note, we investigate the notion of $S$-flat preenvelopes of modules. In particular, we give an example that a ring $R$ being coherent does not imply that every $R$-module have an $S$-flat preenvelope, giving a negative answer to the question proposed by Bennis and Bouziri \cite{BB24}. Besides, we also show that $R_S$ is a coherent ring also does not imply that $R$ is an $S$-coherent ring in general.

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来源期刊

arXiv - MATH - Commutative Algebra

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