S. E. Atani and A. Y. Darani
On primal ideals over semigroups

Let S be a commutative cancellation torsion-free additive semigroup with identity 0 and let S has at least two elements. This paper is devoted to study some properties of primal ideals and quasi-primary ideals of the semigroup S. First, a number of results concerning of these ideals are given. Second, we characterize primal ideals and quasi-primary ideals of a Prufer semigroup and show that in such semigroup, the three concepts: primary, quasi-primary, and primal coincide.

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