Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings

Xiaolei Zhang; Wei Qi

Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings

Commutative Algebra 2026-01-06 v2

Authors: Xiaolei Zhang , Wei Qi

Abstract

In this paper, we give some new characterizations of $u$ - $S$ -Noetherian rings and $u$ - $S$ -coherent rings in terms of uniform $S$ -version of injective precovers, flat preenvelopes and absolutely pure modules, respectively. Moreover, we give a negative answer to a question proposed by Bouziri [3].

Keywords

$u$-$S$-Noetherian ring $u$-$S$-coherent ring injective precover flat preenvelope absolutely pure module

Cite

@article{arxiv.2508.21400,
  title  = {Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings},
  author = {Xiaolei Zhang and Wei Qi},
  journal= {arXiv preprint arXiv:2508.21400},
  year   = {2026}
}

Comments

to appear in Czechoslovak Mathematical Journal

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