An integral domain R is perinormal if every local going-down overring is a localization of R and globally perinormal if every going-down overring is a localization of R. 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 0th graded component.

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