English

A note on $S$-flat preenvelopes

Commutative Algebra 2024-08-21 v1

Abstract

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

Keywords

Cite

@article{arxiv.2408.10523,
  title  = {A note on $S$-flat preenvelopes},
  author = {Xiaolei Zhang},
  journal= {arXiv preprint arXiv:2408.10523},
  year   = {2024}
}