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Lattices with relative Stone congruence lattices. (English) Zbl 1234.06006
Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 81-90 (2010).
It is well known that the congruence lattice of a lattice is in fact a Heyting algebra. In 1958, G. Grätzer and E. T. Schmidt characterized lattices whose congruence lattices are Boolean. In this paper the authors introduce nice conditions under which the congruence lattice of a given lattice is Stone. For this they use conditions (En-modularity and En-separability) which for \(n = 2\) give just a characterization of Boolean congruence lattices.
For the entire collection see [Zbl 1201.08001].

MSC:
06B10 Lattice ideals, congruence relations
06D15 Pseudocomplemented lattices
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