Простые решетки конгруэнций конечных графов
Н.А. Куликов (1990)
Algebra i Logika
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Н.А. Куликов (1990)
Algebra i Logika
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К.В. Адаричева, K. V. Adaričeva, K. V. Adaričeva, K. V. Adaričeva (1996)
Algebra i Logika
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Gerhard Dorfer (2001)
Discussiones Mathematicae - General Algebra and Applications
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In this paper congruences on orthomodular lattices are studied with particular regard to analogies in Boolean algebras. For this reason the lattice of p-ideals (corresponding to the congruence lattice) and the interplay between congruence classes is investigated. From the results adduced there, congruence regularity, uniformity and permutability for orthomodular lattices can be derived easily.
Wiesław Dziobiak, Miklós Maróti, Ralph McKenzie, Anvar Nurakunov (2009)
Fundamenta Mathematicae
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We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if 𝒦 ⊆ ℒ ⊆ ℒ' are quasivarieties of finite signature, and ℒ' is finitely generated while 𝒦 ⊨ WEP, then 𝒦 is finitely axiomatizable relative to ℒ. We prove for any quasivariety 𝒦 that 𝒦 ⊨ RSD(∧) iff 𝒦 has pseudo-complemented congruence lattices and 𝒦 ⊨ WEP. Applying these results and...
Grätzer, G., Schmidt, E.T. (1995)
Beiträge zur Algebra und Geometrie
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А.М. Нуракунов (1990)
Algebra i Logika
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Manfred Armbrust (1973)
Colloquium Mathematicae
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P. Rema (1965)
Fundamenta Mathematicae
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Scott Ahlgren (2003)
Acta Arithmetica
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Marica D. Prešić (1979)
Publications de l'Institut Mathématique
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B. Wojdyło (1973)
Colloquium Mathematicae
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Н.Х. Касымов (1992)
Algebra i Logika
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Hao Pan (2007)
Acta Arithmetica
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Ivan Chajda, Radomír Halaš (2002)
Discussiones Mathematicae - General Algebra and Applications
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We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.
Magill, K.D.jun. (1984)
International Journal of Mathematics and Mathematical Sciences
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