• 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]).