Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 119-129
DOI: https://doi.org/10.7151/dmgaa.1051

ON M-OPERATORS OF q-LATTICES

Radomír Halas

Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ-77900 Olomouc
e-mail: 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 q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.

Keywords: (complete) q-lattice, closure operator, M-operator.

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), 6-12.

[2] I. Chajda and M. Kotrle, Subdirectly irreducible and congruence distributive q-lattices, Czechoslovak Math. J. 43 (1993), 635-642.

[3] I. Chajda, Congruence properties of algebras in nilpotent shifts of varieties, p. 35-46 in: "General Algebra and Discrete Mathematics", Heldermann Verlag, Lemgo 1995.

Received 28 February 2002
Revised 20 September 2002