On atoms in tolerance lattices of distributive lattices
Josef Niederle (1981)
Časopis pro pěstování matematiky
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Josef Niederle (1981)
Časopis pro pěstování matematiky
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Ivan Chajda (1989)
Czechoslovak Mathematical Journal
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Josef Niederle (1980)
Archivum Mathematicum
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Ivan Chajda, Sándor Radelecki (2005)
Commentationes Mathematicae Universitatis Carolinae
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Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz'{e}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.
Sándor Radelecki, Dietmar Schweigert (2004)
Czechoslovak Mathematical Journal
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We characterize lattices with a complemented tolerance lattice. As an application of our results we give a characterization of bounded weakly atomic modular lattices with a Boolean tolerance lattice.