Homomorphisms of implicative semigroups (Q1206773)

A negatively ordered semigroup is an ordered semigroup \(S\) in which the product \(xy\) is a lower bound of \(\{x,y\}\) for all \(x,y\in S\). Such a semigroup is implicative if there is a binary operation \(*: S\to S\) such that \(zx\leq y\Leftrightarrow z\leq x * y\). The authors obtain several results concerning morphisms on such structures, generalizing results of W. C. Nemitz on implicative semilattices and of the reviewer on Brouwer semigroups.