Semigroup rings as almost Prüfer v-multiplication domains

Abstract

Let D be an integral domain with quotient field K, \(\Gamma \) a nonzero torsion-free grading monoid and \(\Gamma ^*=\Gamma {\setminus } \{0\}\). In this paper, we characterize when the semigroup ring \(D[\Gamma ]\) is an almost Prufer v-multiplication domain or an almost Prufer domain. We also give an equivalent condition for the composite semigroup ring \(D+K[\Gamma ^*]\) to be an almost Prufer v-multiplication domain or an almost Prufer domain when \(\Gamma \cap -\Gamma =\{0\}\).