Congruence extension from a semilattice to the freely generated distributive lattice
Isidore Fleischer (1982)
Czechoslovak Mathematical Journal
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Isidore Fleischer (1982)
Czechoslovak Mathematical Journal
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Y.F. Popov (1986)
Semigroup forum
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Miroslav Ploščica, Jiří Tůma, Friedrich Wehrung (1998)
Colloquium Mathematicae
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Isidore Fleischer (1984)
Mathematica Slovaca
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P.V. Ramana Murty, V. Raman (1985)
Mathematica Slovaca
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Pavel Růžička (2008)
Fundamenta Mathematicae
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We prove that there is a distributive (∨,0,1)-semilattice of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from to with 1 in its range, for any algebra A with either a congruence-compatible structure of a (∨,1)-semi-lattice or a congruence-compatible structure of a lattice. In particular, is not isomorphic to the (∨,0)-semilattice of compact congruences of any lattice. This improves Wehrung’s solution of Dilworth’s Congruence Lattice Problem, by giving the best...
K. Auinger (1990)
Semigroup forum
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Zuzana Heleyová (2000)
Discussiones Mathematicae - General Algebra and Applications
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It is known that congruence lattices of pseudocomplemented semilattices are pseudocomplemented [4]. Many interesting properties of congruences on pseudocomplemented semilattices were described by Sankappanavar in [4], [5], [6]. Except for other results he described congruence distributive pseudocomplemented semilattices [6] and he characterized pseudocomplemented semilattices whose congruence lattices are Stone, i.e. belong to the variety B₁ [5]. In this paper we give a partial solution...
Morgado, José (1962)
Portugaliae mathematica
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