Graded Perinormality

TL;DR

This paper introduces graded versions of perinormal and globally perinormal domains, extending existing concepts to graded domains and exploring property descent between graded domains and their degree-zero components.

Contribution

It defines graded perinormality and graded globally perinormality, establishing analogs of known results for these new classes and analyzing property descent.

Findings

Many results for perinormal domains have graded analogs.

Results on property descent between graded domains and their degree-zero parts.

Extension of perinormal concepts to graded algebraic structures.

Abstract

An integral domain $R$ is \emph{perinormal} if every local going-down overring is a localization of $R$ and \emph{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 $0$th graded component.