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A triangular scheme for congruence distributivity. (English) Zbl 0997.08001
Summary: We introduce a triangular scheme for congruences which is satisfied in any congruence distributive algebra $$\mathcal A$$. A condition called Weak Triangular Principle is studied, which is equivalent to the distributivity of Con $$\mathcal A$$ for an arbitrary algebra $$\mathcal A$$. It follows that if $$\mathcal A$$ is congruence permutable then the Triangular Scheme is equivalent to the distributivity of Con $$\mathcal A$$. We define the Triangular Principle as well, which is shown to hold in congruence distributive varieties.

##### MSC:
 08A30 Subalgebras, congruence relations 08B10 Congruence modularity, congruence distributivity
##### Keywords:
congruence distributivity