, Volume 106, Issue 3, pp 205-210

Subsemigroups of finitely generated groups with divisor-theory

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Abstract

In this paper we will characterize all subsemigroups of finitely generated abelian groups, for which there exists a divisor-theory. Besides an explicit geometrical construction of the divisor-theory is given, and it is shown that any finitely generated abelian group occurs as the divisor-class-group of some semigroup.