Global perinormality in a generalized $D + M$ construction

Hannah Klawa

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arXiv · 2211.13412

Global perinormality in a generalized $D + M$ construction

Hannah Klawa

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Abstract

A domain $R$ is \emph{perinormal} if every going-down overring is flat and a perinormal domain $R$ is \emph{globally perinormal} if every flat overring is a localization of $R$ [Epstein-Shapiro 2016]. I show that global perinormality is preserved in a pullback construction which encompasses a classical $D+M$ construction. In doing so, a result is given for the transfer of the property that every flat overring is a localization in the pullback construction considered.

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Hannah Klawa. 2022-11-24. Global perinormality in a generalized $D + M$ construction. https://arxiv.org/abs/2211.13412

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