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ArticleOriginal scientific text

Title

Balanced d-lattices are complemented

Authors 1, 2

Affiliations

  1. Technische Universität Wien, Institut für Algebra und Computermathematik, Wiedner Hauptstraße 8-10/118, A-1040 Wien, Austria
  2. Mathematical Institute, Slovak Academy of Sciences, Gresákova 6, 04001 Košice, Slovakia

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

ENG
balanced congruence, balanced lattice, d-lattice, prime ideal, maximal ideal

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2002/22/1
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Pages:
33-37
Main language of publication
English
Received
2001-12-03
Published
2002

DOI: 10.7151/dmgaa.1045

Exact and natural sciences