On strongly homogeneous prime ideals in a graded integral domain

Abstract

Let [Formula: see text] be a torsionless grading monoid and [Formula: see text] be a [Formula: see text]-graded integral domain. In this paper, we present basic properties and give a complete characterization of strongly homogeneous prime ideals of [Formula: see text]. These works generalize Ahmed and the authors’ characterization of when [Formula: see text] is a graded pseudo-valuation domain.