Proper congruences do not imply a modular congruence lattice
M. G. Stone (1971)
Colloquium Mathematicae
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M. G. Stone (1971)
Colloquium Mathematicae
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Ivan Chajda (1978)
Časopis pro pěstování matematiky
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Iqbalunnisa (1966)
Fundamenta Mathematicae
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Gábor Czédli, Eszter K. Horváth (2002)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Bogdan Staruch, Bożena Staruch (2016)
Bulletin of the Section of Logic
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We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a star-decomposition) is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.
Andrzej Walendziak (2004)
Czechoslovak Mathematical Journal
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In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.
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.