Congruence Pairs of Decomposable MS-Algebras

In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]). They show that every congruence relation θon a decomposable MS-algebra L can be uniquely determined by a congruence pair(θ, θ), where θis a congruence on the de Morgan subalgebra L~??of L and θis a lattice congruence on the sublattice D(L)of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.