Korean J. Math. Vol. 19 No. 3 (2011) pp.255-261
DOI: https://doi.org/10.11568/kjm.2011.19.3.255


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Gyu Whan Chang


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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