Geodesic
Congruence classes in Brouwerian semilattices
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 229-237

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Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.
Keywords: congruence class, Brouwerian semilattice, ideal 
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Chajda, Ivan; Länger, Helmut. Congruence classes in Brouwerian semilattices. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 229-237. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a7/