J. Korean Math. Soc. 2023; 60(3): 521-536
Online first article April 13, 2023 Printed May 1, 2023
https://doi.org/10.4134/JKMS.j220055
Copyright © The Korean Mathematical Society.
Xiaolei Zhang
Shandong University of Technology
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 $u$-$S$-pure $u$-$S$-exact sequences and uniformly $S$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then we characterize uniformly $S$-von Neumann regular rings and uniformly $S$-Noetherian rings using uniformly $S$-absolutely pure modules.
Keywords: $u$-$S$-pure $u$-$S$-exact sequence, uniformly $S$-absolutely pure module, uniformly $S$-von Neumann regular ring, uniformly $S$-Noetherian ring
MSC numbers: 16U20, 13E05, 16E50
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