Weakly atomic lattices with Stonean congruence lattice
Sándor Radelecki (2002)
Mathematica Slovaca
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Sándor Radelecki (2002)
Mathematica Slovaca
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E. Lopez-Escobar (1966)
Fundamenta Mathematicae
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M. G. Stone (1971)
Colloquium Mathematicae
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Iqbalunnisa (1971)
Fundamenta Mathematicae
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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.
Juhani Nieminen (1978)
Archivum Mathematicum
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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.