Abstract. We introduce a triangular scheme for congruences which is satisfied in any congruence distributive algebra ${\cal A}$. A condition called Weak Triangular Principle is studied, which is equivalent to the distributivity of ${\mathop{\rm Con} {\cal A}}$ for an arbitrary algebra ${\cal A}$. It follows that if ${\cal A}$ is congruence permutable then the Triangular Scheme is equivalent to the distributivity of $ {\mathop{\rm Con} {\cal A}}$. We define the Triangular Principle as well, which is shown to hold in congruence distributive varieties.

AMS Subject Classification (1991): 08A30, 08B10

Keyword(s): congruence distributivity, congruence permutability, Shifting Lemma, Triangular Scheme, Triangular Principle

Received October 30, 2000, and in final form July 7, 2001. (Registered under 2826/2009.)