A coordinatisation of implicative (semi-)lattices by Baer semigroups
T. S. Blyth · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1978
Synopsis We show that if L is a bounded (semi-)lattice and f is a range-closed idempotent residuated mapping on L then f is multiplicative if and only if it is decreasing. We then use this to prove that a bounded (semi-)lattice is implicative if and only if it can be coordinatised by a weakly multiplicative (right) Baer semigroup.