Permutabitity of principal $ MS $-algebras

Abstract

<abstract><p>In this paper, we continue to introduce new properties of principal $ MS $-algebras deal with congruence relations via $ MS $-congruence pairs. Necessary and sufficient conditions for a pair of congruences $ (\theta_{1}, \theta_{2})\in Con(L^{\circ\circ})\times Con_{lat}(D(L)) $ to become an $ MS $-congruence pair of a principal $ MS $-algebra (principal Stone algebra) $ L $ are obtained. We describe the lattice of all $ MS $-congruence pairs of a principal $ MS $-algebra $ L $ which induced by the Boolean elements of $ L $. We introduce certain special congruence $ \Psi $ on a principal $ MS $-algebra and its related properties which are useful for the topic of this paper. A characterization of $ 2 $-permutable congruences using $ MS $-congruence pairs of principal $ MS $-algebras is established. Finally, a characterization of $ n $-permutability of congruences of principal $ MS $-algebras is given, which is a generalization of the characterization of $ 2 $-permutability of congruences of such algebras.</p></abstract>