Singular antitone systems (Q1304913)

An antitone system is an ordered set \((P;\leq)\) together with an antitone mapping \(g:P\to P\). Given an ordered set \(P\) and an antitone mapping \(g:P\to P\), the scope of this paper is to give necessary and sufficient conditions for the existence of an odd positive integer \(k\) such that \(g^k\) is isotone. The result obtained has natural applications to the dual space of an Ockham algebra. In particular, the authors determine the cardinality of the endomorphism semigroup of a finite subdirectly irreducible Ockham algebra.