Global perinormality in a generalized D + M construction

Abstract

A domain R is perinormal if every going-down overring is flat and a perinormal domain R is globally perinormal if every flat overring is a localization of R [2]. 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.

Communicated by Scott Chapman

KEYWORDS:

• D + M constructions
• flat overrings
• globally perinormal domains
• localizations
• pullbacks

2020 MATHEMATICS SUBJECT CLASSIFICATION Primary:

• 13G05
• Secondary: 13A15
• 13B30
• 13F05

Acknowledgments

I am very grateful to my advisor Neil Epstein for suggesting the question which led to this work and for helpful advice and input along the way. I am also grateful to Evan Houston for catching an error in a previous version of the paper and the referee for helpful comments which improved the paper.