A note on perinormal domains

Abstract

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Recently, N. Epstein and J. Shapiro introduced and studied the perinormal domains: those domains $A$ whose overrings satisfying going down over $A$ are flat $A$-modules. We show that every Prufer v-multiplication domain is perinormal and has no proper lying over overrings. Conversely, we show that a w-treed perinormal domain is a Prufer v-multiplication domain. We give two pull-back constructions that produce perinormal/non-perinormal domains.