Mathematicae General Algebra and Applications 22(2) (2002)
ON M-OPERATORS OF q-LATTICES
Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ-77900 Olomouc
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.
I. Chajda, Lattices on quasiordered sets, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 31
I. Chajda and M. Kotrle, Subdirectly irreducible and congruence distributive q-lattices,
Czechoslovak Math. J. 43 (1993), 635-642.
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