Geodesic
Congruences on semilattices with section antitone involutions
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 207-215 Cet article a éte moissonné depuis la source Library of Science

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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/

[1] J.C. Abbott, Semi-boolean algebras, Matem. Vestnik 4 (1967), 177-198.

[2] J.C. Abbott, Orthoimplication algebras, Studia Logica 35 (1976), 173-177. doi: 10.1007/BF02120879

[3] I. Chajda, Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carol. 44 (2003), 577-585.

[4] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag (Lemgo, Germany), 220pp., 2003, ISBN 3-88538-226-1.

[5] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 228pp., 2007, ISBN 978-3-88538-230-0.

[6] I. Chajda, R. Halaš and J. Kühr, Implication in MV-algebras, Algebra Universalis 53 (2005), 377-382. doi: 10.1007/s00012-004-1862-4