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Balanced d-lattices are complemented

Martin Goldstern·Miroslav Ploscica
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Abstract

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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Martin Goldstern, Miroslav Ploscica. 2001-11-27. Balanced d-lattices are complemented. https://arxiv.org/abs/math/0111282

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