Hypersubstitutions in orthomodular lattices

• Autorzy: Ivan Chajda , Helmut Länger
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hypersubstitution; proper hypersubstitution; orthomodular lattice; absorption algebra

Kategorie tematyczne

• 08A40: Operations, polynomials, primal algebras
• 06C15: Complemented lattices, orthocomplemented lattices and posets

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 83-92

Daty

wydano

2001

otrzymano

2000-02-01

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, CZ-77900 Olomouc, Czech Republic

autor

Helmut Länger

• Technische Universität Wien, Institut für Algebra und Computermathematik, Wiedner Hauptstraße 8-10, A-1040 Wien

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1029