DETERMINED CONGRUENCE CLASSES IN BROUWERIAN SEMILATTICES

Ivan Chajda; Josef Zedn´ık

Ivan Chajda
Josef Zedn´ık

Keywords: Brouwerian semilattice, regularity of congruences, congruence class, relative pseudocomplement

Abstract

Let Θ be a congruence of an algebra A =(A,F) anda,b ∈ A. We say that the class [a]Θ determines [b]Θ if for each Φ∈ Con A,[ b]Φ =[ b]Θ whenever [a]Φ =[a]Θ. We characterize those classes [a]Θ of a Brouwerian semilattice which determine [b]Θ for b ≤ a.