Multiplicative Ideal Theory of Semigroups

抄録

The multiplicative ideal theory has been developped for commutative rings. The aim of this paper is to give a semigroup version of the multiplicative ideal theory of commutative rings. In this paper we shall prove some fundamental properties of ideals of G-semigroups. Here we call a torsion-free cancellative abelian additive semigroup with identity a G-semigroup, where G stands for Gilmer. It is expected that the ideal theory of G-semigroups is more simpler than that of commutative rings. But the multiplicative ideal theory of semigroups is itself interesting and important. For the multiplicative ideal theory of rings, we refer to [Gl] and [LM].