The hull-kernel topology on prime ideals in ordered semigroups

Abstract

The aim of this study is to develop the theory of prime ideals in ordered semigroups. First, to ensure the existence of prime ideals, we study a class of ordered semigroups which will be denoted by SIP{{\mathbb{S}}}_{IP}. And then we introduce the hull-kernel topology for the prime ideals P(S){\mathcal{P}}\left(S) and the topological properties like separation axioms, compactness and connectedness are studied. Finally, we focus on the subspace ℳ(S,I){\mathcal{ {\mathcal M} }}\left(S,I), minimal prime ideals containing the ideal II in an ordered semigroup SS. We investigate topological properties of this subspace and connections between this subspace and the ordered semigroup SS.

Keywords

• ordered semigroup
• ideal
• prime ideal
• minimal prime ideal
• hull-kernel topology
• 06f05