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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.

08A30 Subalgebras, congruence relations
08B10 Congruence modularity, congruence distributivity