SEMIGROUP RINGS AS H-DOMAINS

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.