Perinormality in pullbacks

We further develop the notion of perinormality from our last paper, showing that it is preserved by many pullback constructions. In doing so, we introduce the concepts of relative perinormality and fragility for ring extensions.
Comment: Major revision. Due to an error in the main theorem of section 3 in version 1, we have reworked the notion of fragility into three potentially separate notions. There are several related new localization results. Several other things in the paper have changed a bit, most notably Corollary 2.6 (also now corrected). 18 pages, comments welcome