Strong congruence in atomistic lattices
H. S. Ramananda · Acta Mathematica Universitatis Comenianae · 2016
In this paper, for an atomistic lattice L satisfying the ascending and descending chain conditions, it is proved that • the congruence lattice Con L is isomorphic to the sublattice of the set of all standard elements of L; • every congruence relation of L is representable. Further, the notion of a strong congruence relation in lattices is introduced, some examples of strong congruence relations are given and it is proved that in a sectionally complemented lattice satisfying the ascending and descending chain conditions, every congruence relation is strong.