Modal semilattices, implicative semilattices and triples (Q2759831)

All semilattices in the paper are meet semilattices with unit. A semilattice equipped with a multiplicative closure operator is called a modal semilattice. A triple is a system \((C,D,f)\), where \(C\) and \(D\) are semilattices and \(f\) is an order-reversing homomorphism from \(C\) into \(\text{End} D\). A bijective correspondence between the class of triples and a certain subclass of the modal semilattices is established. Further, implicative modal semilattices belonging to that subclass are characterized in terms of so-called implicative triples. In this way, several results known for pseudocomplemented semilattices are extended.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].