Scholarlink

<p>We investigate the notion of <i>S</i>-flat preenvelopes of modules. In particular, we give an example that a ring <i>R</i> being coherent does not imply that every <i>R</i>-module has an <i>S</i>-flat preenvelope, giving a negative answer to the question proposed by D. Bennis and A. Bouziri (2025). Besides, we also show that a ring <i>R</i><sub><i>S</i></sub> being coherent also does not imply that <i>R</i> is an <i>S</i>-coherent ring in general.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A note on S-flat preenvelopes

  • 期刊论文

  • 发表日期：

    2025年5月19日

查看全文
  • Xiaolei Zhang

摘要

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 has an S-flat preenvelope, giving a negative answer to the question proposed by D. Bennis and A. Bouziri (2025). Besides, we also show that a ring RS being coherent also does not imply that R is an S-coherent ring in general.