Geodesic
Congruences on semilattices with section antitone involutions
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 207-215

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We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
Keywords: semilattice, section, antitone involution, congruence kernel, filter, congruence distributivity, 3-permutability 
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Chajda, Ivan. Congruences on semilattices with section antitone involutions. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 207-215. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a4/