Journal of the
Korean Mathematical Society JKMS

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