### Congruence Topologies on Universal Algebras.

Sydney Bulman-Fleming (1971)

Mathematische Zeitschrift

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Sydney Bulman-Fleming (1971)

Mathematische Zeitschrift

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Manfred Armbrust (1973)

Colloquium Mathematicae

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Scott Ahlgren (2003)

Acta Arithmetica

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John H. Hodges (1966)

Mathematische Zeitschrift

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Marica D. Prešić (1979)

Publications de l'Institut Mathématique

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Hao Pan (2007)

Acta Arithmetica

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Ying Zhang (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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L. Carlitz (1960)

Mathematische Annalen

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Alfred L. Foster (1970)

Mathematische Zeitschrift

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Leonard Eugene Dickson (1901)

Mathematische Annalen

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E. Nazarewicz, M. O&amp;#039;Brien, M. O&#039;Neill, C. Staples (2007)

Acta Arithmetica

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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.

F. Rudolf Beyl (1986)

Mathematische Zeitschrift

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Ivan Chajda, Günther Eigenthaler (2001)

Discussiones Mathematicae - General Algebra and Applications

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It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity...

Józef Słomiński (1974)

Colloquium Mathematicae

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A. Schinzel (2015)

Acta Arithmetica

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Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.