Discussiones
Mathematicae General Algebra and Applications 22(2) (2002)
119129
doi: 10.7151/dmgaa.1051
ON MOPERATORS OF qLATTICES
Radomír Halas
Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ77900 Olomouc
email: halas@aix.upol.cz
Abstract
It is well known that every complete lattice can be considered as a complete lattice of closed sets with
respect to appropriate closure operator. The theory of qlattices as a natural generalization of lattices
gives rise to a question whether a similar statement is true in the case of qlattices. In the paper the
socalled Moperators are introduced and it is shown that complete qlattices are qlattices of closed sets
with respect to Moperators.
Keywords: (complete) qlattice, closure operator, Moperator.
2000 Mathematics Subject Classification: 06B99, 05A05, 06A15.
References
[1]
I. Chajda, Lattices on quasiordered sets, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 31
(1992), 612.

[2]
I. Chajda and M. Kotrle, Subdirectly irreducible and congruence distributive qlattices,
Czechoslovak Math. J. 43 (1993), 635642.

[3]
I. Chajda, Congruence properties of algebras in nilpotent shifts of varieties, p. 3546 in: "General
Algebra and Discrete Mathematics", Heldermann Verlag, Lemgo 1995.

Received 28 February 2002
Revised 20 September 2002