2001/11/27 by Martin Goldstern, Goldstern, Martin, Miroslav Ploščica +2
Computer Science · Mathematics · #06B10 #08A30 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B10 #msc:08A30
paper · pdf · doi:10.48550/arxiv.math/0111282
4 pages, LaTeX2e
arxiv created 2001/11/27 · openalex publication_date 2001/11/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.