Abstract

Here we initiate an investigation of the equational classes of Ockham algebras endowed with a quantifier and of monadic distributive lattioes endowed with a dual endomorphism . These varieties are natural generalizations of the Q-distributive lattices introduced by R. Cignoli and the monadic the De Morgan algebras considered by A. Petrovich, respectively. Our main interest is the duality theory for each of these classes of algebras. In order to do this, we require Urquart's duality for Ockham algebras and Goldblatt's duality for bounded distributive lattices with operations. The dualities enable us to describe the lattices of congruences on OQ-algebras and MOL-algebras. Finally, some results for pseudocomplemented. MOL-algebras and monadic Heyting algebras endowed with a dual endomorphism are announced