Abstract. Weakly associative lattices, a generalization of lattices, led to the introduction of dual discriminator. For a further generalization, graph algebras (or weak lattices), the original term did not produce a ``suitable'' term for dual discriminator function. Our goal is to describe why the original term was applicable for weakly associative lattices, and we present a class of algebras where the original term yields the dual discriminator function.

AMS Subject Classification (1991): 06B99, 08B99

Keyword(s): varieties, dual discriminator function, generalizations of lattices, directed graphs, projective planes

Received February 6, 2003, and in final form April 16, 2006. (Registered under 5931/2009.)