Geodesic
Semilattices with sectional mappings
Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 11-19 Cet article a éte moissonné depuis la source Library of Science

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We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].
Keywords: semilattice, sectional mapping, antitone mapping, switching mapping, involution 
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Chajda, Ivan; Eigenthaler, Günther. Semilattices with sectional mappings. Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 11-19. http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a0/

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

[2] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003, pp. 217.

[3] I. Chajda and P. Emanovský, Bounded lattices with antitone involutions and properties of MV-algebras, Discussiones Mathem., General Algebra and Appl. 24 (1) (2004), 31-42.

[4] I. Chajda, R. Halaš and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19-33.