Displaying similar documents to “Varieties satisfying the triangular scheme need not be congruence distributive”

On schemes for congruence distributivity

I. Chajda, R. Halaš (2004)

Open Mathematics

Similarity:

We present diagrammatic schemes characterizing congruence 3-permutable and distributive algebras. We show that a congruence 3-permutable algebra is congruence meetsemidistributive if and only if it is distributive. We characterize varieties of algebras satisfying the so-called triangular scheme by means of a Maltsev-type condition.

Congruence submodularity

Ivan Chajda, Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

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.