On uniformly $S$-absolutely pure modules

Xiaolei Zhang

On uniformly $S$-absolutely pure modules

Commutative Algebra 2022-05-25 v2

Authors: Xiaolei Zhang

Abstract

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$ . In this paper, we introduce and study the notions of $S$ -pure $S$ -exact sequences and $S$ -absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then we characterize $S$ -von Neumann regular rings and uniformly $S$ -Noetherian rings using $S$ -absolutely pure modules.

Keywords

module theory module categories commutative ring theory

Cite

@article{arxiv.2108.06851,
  title  = {On uniformly $S$-absolutely pure modules},
  author = {Xiaolei Zhang},
  journal= {arXiv preprint arXiv:2108.06851},
  year   = {2022}
}

Related papers

View all related →