Graded perinormality

Abstract

An integral domain [Formula: see text] is perinormal if every local going-down overring is a localization of [Formula: see text] and globally perinormal if every going-down overring is a localization of [Formula: see text]. In this paper, I introduce notions of graded perinormal and graded globally perinormal domains and show that many results obtained for perinormal and globally perinormal domains have graded analogs. I also give some results for descent of properties between a graded domain and its [Formula: see text]th graded component.