Perinormality in pullbacks

Abstract

In previous work, we introduced the notion of perinormality and showed how it lies in the greater context of commutative algebra, fitting as it does between the class of Krull domains and the class of seminormal ($R_1$) domains. Here we develop the concept further, using several pullback (i.e., gluing) constructions that yield perinormal domains. In doing so, we introduce the concepts of relative perinormality and fragility for ring extensions, which we believe to be of independent interest.