Discussiones
Mathematicae General Algebra and Applications 21(1) (2001) 83-92
DOI: https://doi.org/10.7151/dmgaa.1029
HYPERSUBSTITUTIONS IN ORTHOMODULAR LATTICES
Ivan Chajda Department of Algebra and Geometry |
Helmut Länger Technische Universität Wien |
Abstract
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.
2000 Mathematics Subject Classification: 08A40, 06C15.
References
| [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, p. 106-115 in: ``General Algebra and Ordered Sets (Horni Lipová 1994)", Palacký University, Olomouc 1994. |
| [6] | J. Płonka, On hyperidentities of some varieties, p. 199-213 in: ``General Algebra and Discrete Mathematics (Potsdam 1993)", Heldermann-Verlag, Lemgo 1995. |
| [7] | Z. Szylicka, Proper hypersubstitutions of normalizations and externalizations of varieties, p. 144-155 in: ``General Algebra and Ordered Sets (Horni Lipová 1994)", Palacký University, Olomouc 1994. |
| [8] | W. Taylor, Hyperidentities and hypervarieties, Aequationes Math. 23 (1981), 30-49. |
Received 1 February 2000
Close