Geodesic
Semilattices with sectional mappings
Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 11-19.

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGAA_2007_27_1_a0,
     author = {Chajda, Ivan and Eigenthaler, G\"unther},
     title = {Semilattices with sectional mappings},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {11--19},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a0/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Eigenthaler, Günther
TI  - Semilattices with sectional mappings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2007
SP  - 11
EP  - 19
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a0/
LA  - en
ID  - DMGAA_2007_27_1_a0
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Eigenthaler, Günther
%T Semilattices with sectional mappings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2007
%P 11-19
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a0/
%G en
%F DMGAA_2007_27_1_a0
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.