Conditions for permutability of congruences in implication algebras

Abstract

In this paper we give conditions on an implication algebra A so that two congruences θ1, θ2 on A permute, i.e. θ1 ○ θ2 = θ2 ○ θ1. We also provide simpler conditions for permutability in finite implication algebras. Finally we present some applications of these characterizations.