Geodesic
Strong congruence in atomistic lattices
H. S. Ramananda1 ; H. S. Ramananda
1Department of Mathematics, St. Joseph Engineering College,, Vamanjoor, Mangalore, Karnataka State, India
Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 2, pp. 337-346 
H. S. Ramananda; H. S. Ramananda. Strong congruence in atomistic lattices. Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 2, pp. 337-346. http://geodesic.mathdoc.fr/item/AMUC_2016_85_2_a12/
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     title = { Strong congruence in atomistic lattices},
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     pages = {337--346},
     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/AMUC_2016_85_2_a12/}
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Voir la notice de l'article provenant de la source Comenius University

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.