| Sumario: | A Q-distributive lattice is an algebra 〈L, ∧, ∨, ∇, 0, 1〉 of type (2, 2, 1, 0, 0) such that 〈L, ∧, ∨, 0, 1〉 is a bounded distributive lattice and ∇ satisfies the equations: (1) ∇0 = 0, (2) x ∧ ∇x = x, (3) ∇(x ∧ ∇y) = ∇x ∧ ∇y and (4) ∇(x ∨ y) = ∇x ∨ ∇y. The opposite of the category of Q-distributive lattices is described in terms of Priestly spaces endowed with an equivalence relation. The simple and the sub-directly irreducible Q-distributive lattices are determined and it is shown that the lattices of equational classes of Q-distributive lattices is a chain of type ω + 1. © 1991.
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