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

[BIBTex] [PDF] [PS]

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