Geodesic
Hypersubstitutions in orthomodular lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 83-92 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.
Keywords: hypersubstitution, proper hypersubstitution, orthomodular lattice, absorption algebra 
@article{DMGAA_2001_21_1_a7,
     author = {Chajda, Ivan and L\"anger, Helmut},
     title = {Hypersubstitutions in orthomodular lattices},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {83--92},
     year = {2001},
     volume = {21},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a7/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Länger, Helmut
TI  - Hypersubstitutions in orthomodular lattices
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2001
SP  - 83
EP  - 92
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a7/
LA  - en
ID  - DMGAA_2001_21_1_a7
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Länger, Helmut
%T Hypersubstitutions in orthomodular lattices
%J Discussiones Mathematicae. General Algebra and Applications
%D 2001
%P 83-92
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a7/
%G en
%F DMGAA_2001_21_1_a7
Chajda, Ivan; Länger, Helmut. Hypersubstitutions in orthomodular lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 83-92. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a7/

[1] I. Chajda and K. Głazek, A Basic Course on General Algebra, Technical University Press, Zielona Góra 2000.

[2] K. Denecke, D. Lau, R. Pöschel, and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Contribution to General Algebra 7 (1991), 97-118.

[3] E. Graczyńska and D. Schweigert, Hypervarieties of a given type, Algebra Universalis 27 (1990), 305-318.

[4] R. Padmanabhan and P. Penner, Bases of hyperidentities of lattices, C.R. Math. Rep. Acad. Sci. Canada 4 (1982), 9-14.

[5] J. Płonka, Proper and inner hypersubstitutions of varieties, 'General Algebra and Ordered Sets (Horni Lipová 1994)', Palacký University, Olomouc 1994, 106-115.

[6] J. Płonka, On hyperidentities of some varieties, 'General Algebra and Discrete Mathematics (Potsdam 1993)', Heldermann-Verlag, Lemgo 1995, 199-213.

[7] Z. Szylicka, Proper hypersubstitutions of normalizations and externalizations of varieties, 'General Algebra and Ordered Sets (Horni Lipová 1994)', Palacký University, Olomouc 1994, 144-155.

[8] W. Taylor, Hyperidentities and hypervarieties, Aequationes Math. 23 (1981), 30-49.