The space of minimal prime ideals in a 0-distributive semilattice (Q788753)

This paper is a continuation of the study of minimal prime ideals in a 0- distributive semilattice initiated in an earlier paper of the authors [ibid. 237-246 (1982; reviewed above)] and is mainly concerned with the space \({\mathfrak M}\) of minimal prime ideals with the hull kernel topology. It is proved that \({\mathfrak M}\) is Hausdorff. Several necessary and sufficient conditions for \({\mathfrak M}\) to be compact are derived. A representation theorem (like Stone's theorem for Boolean algebras) for disjunctive 0-distributive semilattices is obtained.