• Korean Journal of Mathematics
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• v.19 no.3
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• pp.255-261
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• 2011

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, ${\ldots}$), 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 $\mathbb{R}$ is the eld of real numbers and if ${\Gamma}$ is the additive group of rational numbers, then $\mathbb{R}[{\Gamma}]$ is not an H-domain.

• East Asian mathematical journal
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• v.22 no.2
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• pp.189-194
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• 2006

Throughout this paper, a semigroup S will denote a torsion free grading monoid, and it is a non-zero semigroup with 0. The operation is written additively. The aim of this paper is to study semigroup version of an integral domain ([1],[3],[4] and [5]).