Some Properties of Valuation Ideals and Primary Ideals in Additive Semigroups: M. Yahya Abbasi, Abul Basar - Team, Support (Thai Journal of Mathematics, 2019)
This paper deals with the connections and interdependencies among prime ideals, primary ideals, valuation ideals, valuation semigroups and semigroups. R. Gilmer and J. Ohm [1] studied primary ideals and valuation ideals for integral domains. In this article, we generalize this concept for semigroups. It is proved that if T is a prime ideal of a semigroup S, and {Q_α } is the set of primary ideals that belongs to T. Further, if I=Q_α and every Q_α is a valuation ideal, then I is prime.