Balanced d-lattices are complemented

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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.
4 pages, LaTeX2e

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Rings and Algebras, 06B10; 08A30

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http://salesiana.dossiersoluciones.com/handle/123456789/62742

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0111282
 http://arxiv.org/abs/math/0111282

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arXiv