Abstract. We prove that if ${\cal V}$ is a variety with factorable congruences in which every member can be represented as a Boolean product of directly indecomposable algebras, then ${\cal V}$ is a discriminator variety.

AMS Subject Classification (1991): 08A05, 08A30, 08A40, 08B10; 06E15

Keyword(s): Boolean product, discriminator variety, factorable congruences, Boolean factor congruences, Pierce sheaf, principal congruence formula

Received January 5, 1994 and in revised form May 23, 1996. (Registered under 6120/2009.)