Hypersubstitutions in orthomodular lattices
Ivan Chajda ; Helmut Länger
Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001), p. 83-92 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:287606 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1029,
     author = {Ivan Chajda and Helmut L\"anger},
     title = {Hypersubstitutions in orthomodular lattices},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {21},
     year = {2001},
     pages = {83-92},
     zbl = {0996.08003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1029}
}

Ivan Chajda; Helmut Länger. Hypersubstitutions in orthomodular lattices. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 83-92. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1029/

[000] [1] I. Chajda and K. Głazek, A Basic Course on General Algebra, Technical University Press, Zielona Góra 2000. | Zbl 0970.08001

[001] [2] K. Denecke, D. Lau, R. Pöschel, and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Contribution to General Algebra 7 (1991), 97-118. | Zbl 0759.08005

[002] [3] E. Graczyńska and D. Schweigert, Hypervarieties of a given type, Algebra Universalis 27 (1990), 305-318. | Zbl 0715.08002

[003] [4] R. Padmanabhan and P. Penner, Bases of hyperidentities of lattices, C.R. Math. Rep. Acad. Sci. Canada 4 (1982), 9-14. | Zbl 0478.06004

[004] [5] J. Płonka, Proper and inner hypersubstitutions of varieties, 'General Algebra and Ordered Sets (Horni Lipová 1994)', Palacký University, Olomouc 1994, 106-115.

[005] [6] J. Płonka, On hyperidentities of some varieties, 'General Algebra and Discrete Mathematics (Potsdam 1993)', Heldermann-Verlag, Lemgo 1995, 199-213. | Zbl 0813.08004

[006] [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. | Zbl 0828.08004

[007] [8] W. Taylor, Hyperidentities and hypervarieties, Aequationes Math. 23 (1981), 30-49. | Zbl 0491.08009