A note on $\phi$-Pr\"ufer $v$-multiplication rings

Xiaolei Zhang

A note on $\phi$-Pr\"ufer $v$-multiplication rings

Commutative Algebra 2021-07-27 v1

Authors: Xiaolei Zhang

Abstract

In this note, we show that a strongly $\phi$ -ring $R$ is a $\phi$ -PvMR if and only if any $\phi$ -torsion free $R$ -module is $\phi$ - $w$ -flat, if and only if any divisible module is nonnil-absolutely $w$ -pure module, if and only if any $h$ -divisible module is nonnil-absolutely $w$ -pure module, if and only if any finitely generated nonnil ideal of $R$ is $w$ -projective.

Keywords

module theory commutative ring theory

Cite

@article{arxiv.2107.11907,
  title  = {A note on $\phi$-Pr\"ufer $v$-multiplication rings},
  author = {Xiaolei Zhang},
  journal= {arXiv preprint arXiv:2107.11907},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2103.08278

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