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 theta on a decomposable MS-algebra L can be uniquely determined by a congruence pair (theta(1),theta(2)), where theta(1) is a congruence on the de Morgan subalgebra L degrees degrees of L and theta(2) is 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.