Congruence Pairs of Decomposable MS-Algebras*

Citation:

Sanaa El-ASSAR,Abd El-Mohsen BADAWY.Congruence Pairs of Decomposable MS-Algebras*[J].Chinese Annals of Mathematics B,2021,42(4):561~574
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Authors:

Sanaa El-ASSAR; Abd El-Mohsen BADAWY

Foundation:

2nd International Conference for Mathematics, Statistics and Information Technology (ICMSIT for short) that held in the Faculty of Science, Tanta University, Egypt, 18-20 December, 2018.
Abstract: 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 θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1, θ2), where θ1 is a congruence on the de Morgan subalgebra L?? of L and θ2 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.

Keywords:

MS-Algebras, Decomposable MS-algebras, Congruence pairs, Strong extension, Permutability, Congruence lattices

Classification:

06D05, 06D30
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