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Discussiones Mathematicae General Algebra and Applications 22(1) (2002) 33-37
DOI: https://doi.org/10.7151/dmgaa.1045

BALANCED d-LATTICES ARE COMPLEMENTED

Martin Goldstern Technische Universität Wien Institut für Algebra und Computermathematik Wiedner Hauptstraße 8-10/118, A-1040 Wien, Austria e-mail: martin.goldstern@tuwien.ac.at http://www.tuwien.ac.at/goldstern/

Miroslav Ploscica  Mathematical Institute, Slovak Academy of Sciences Gresákova 6, 04001 Kosice, Slovakia e-mail: ploscica@saske.sk http://www.saske.sk/MI/eng/ploscica.htm

Abstract

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

 Keywords: balanced congruence, balanced lattice, d-lattice, prime ideal, maximal ideal.

 2000 AMS Mathematics Subject Classifications: 06B10, 08A30.

 References

 

[1] I. Chajda and G. Eigenthaler, Balanced congruences, Discuss. Math. - Gen. Algebra App. 21 (2001), 105-114.

[2] G. Grätzer, General Lattice Theory (the second edition), Birkhäuser Verlag, Basel 1998.

Received 3 December 2001