Discussiones Mathematicae General Algebra and Applications 21(2) (2001) 229-237
doi: 10.7151/dmgaa.1040

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CONGRUENCE CLASSES IN BROUWERIAN SEMILATTICES

Ivan Chajda

Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ-77900 Olomouc
e-mail: chajda@risc.upol.cz

Helmut Länger

Technische Universität Wien
Institut für Algebra und Computermathematik
Wiedner Hauptstraß e 8-10, A-1040 Wien
e-mail: h.laenger@tuwien.ac.at

Abstract

Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with aŮc Ł b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.

Keywords: congruence class, Brouwerian semilattice, ideal.

2000 Mathematics Subject Classification: Primary 08A30; Secondary 06A12.

References

[1]J. Duda, Arithmeticity at 0, Czechoslovak Math. J. 37 (1987), 197-206.
[2] K. Fichtner, Eine Bemerkung über Mannigfaltigkeiten universeller Algebren mit Idealen, Monatsb. Deutsch. Akad. Wiss. Berlin 12 (1970), 21-25.
[3] P. Köhler, Brouwerian semilattices: the lattice of total subalgebras, Banach Center Publ. 9 (1982), 47-56.
[4] W.C. Nemitz, Implicative semi-lattices, Trans. Amer. Math. Soc. 117 (1965), 128-142.

Received 14 August 2001
Revised 12 December 2001