Balanced d-lattices are complemented

Details Balanced d-lattices are complemented Balanced d-lattices are complemented

2001-11-27

arxiv.org/abs/math/0111282v1

Mathematics

Rings and Algebras

4 pages, LaTeX2e

Scientific paper

We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is the characterization of d-lattices (a class of bounded lattices including the bounded distributive lattices, originally defined by a property of their compact congruences) as exactly those lattices in which all maximal filters/ideals are prime.

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