On graded pseudo-valuation domains

Abstract

Let Γ be a torsionless commutative cancellative monoid and be a Γ-graded integral domain. In this paper, we provide necessary and sufficient conditions for R to be a graded pseudo-valuation domain. In particular, we determine when the semigroup ring over an integral domain D is a graded pseudo-valuation domain. Also some connections of graded pseudo-valuation domains and UMT-domains are studied.