Semigroup rings as H-domains
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Let D be an integral domain, S be a torsion-free grading monoid such that the quotient group of S is of type (0,0,0,...), and D[S] be the semigroup ring of S over D. We show that D[S] is an H-domain if and only if D is an H-domain and each maximal t-ideal of S is a v-ideal. We also show that if R is the field of real numbers and if Γ is the additive group of rational numbers, then R[Γ] is not an H-domain.
Abstract
Let D be an integral domain, S be a torsion-free grading monoid such that the quotient group of S is of type (0,0,0,...), and D[S] be the semigroup ring of S over D. We show that D[S] is an H-domain if and only if D is an H-domain and each maximal t-ideal of S is a v-ideal. We also show that if R is the field of real numbers and if Γ is the additive group of rational numbers, then R[Γ] is not an H-domain.
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