On graded Going down domains

Abstract

Let $\hat{I}“$ be a torsionless commutative cancellative monoid and $R={⨁}_{\hat{I}\pm \in \hat{I}“}{R}_{\hat{I}}\pm$ be a $\hat{I}“$-graded integral domain. In this paper, we introduce the notion of graded going-down domains. Among other things, we provide an equivalent condition for graded-Prüfer domains in terms of graded going-down and graded finite-conductor domains. We also characterize graded going-down domains by means of graded divided domains. As an application, we show that the graded going-down property is stable under factor domains.

Final version, to appear in JAA