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arXiv · 2107.11907

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

Xiaolei Zhang
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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.

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Xiaolei Zhang. 2021-07-25. A note on $\phi$-Pr\"ufer $v$-multiplication rings. https://arxiv.org/abs/2107.11907

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