Abstract. We use some commutator theory together with a recent result by K. Kearnes and A. Szendrei in order to provide a non-trivial implication between two congruence identities strictly weaker than modularity.

AMS Subject Classification (1991): 08B99, 06B20, 08A30, 08B10

Keyword(s): Congruence (lattice) identities, congruence modularity, weak difference term, commutator of congruences

Received April 29, 1999, and in revised form April 23, 2000. (Registered under 2858/2009.)