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].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1115,
author = {Ivan Chajda and G\"unther Eigenthaler},
title = {Semilattices with sectional mappings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {27},
year = {2007},
pages = {11-19},
zbl = {1138.06002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1115}
}
Ivan Chajda; Günther Eigenthaler. Semilattices with sectional mappings. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 11-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1115/
[000] [1] J.C. Abbott, Semi-Boolean algebras, Matem. Vestnik 4 (1967), 177-198. | Zbl 0153.02704
[001] [2] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003, pp. 217. | Zbl 1014.08001
[002] [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. | Zbl 1082.03055
[003] [4] I. Chajda, R. Halaš and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19-33. | Zbl 1099.06006