Local versions of some congruence properties in single algebras

Ivan Chajda; Gerhard Dorfer; Helmut Länger

Displaying similar documents to “Local versions of some congruence properties in single algebras”

Semiregularity of congruences implies congruence modularity at 0

Ivan Chajda (2002)

Czechoslovak Mathematical Journal

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We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of $𝒜 \times 𝒜$ is semiregular then $𝒜$ is congruence modular at 0.

Trapezoid lemma and congruence distributivity

Ivan Chajda, Gábor Czédli, Eszter K. Horváth (2003)

Mathematica Slovaca

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The Csákány theory of regularity for finite algebras

Ivan Chajda (1995)

Mathematica Slovaca

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Some modifications of congruence permutability and dually congruence regular varietie

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...

Some properties of congurence relations on orthomodular lattices

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.