Abstract. A variety ${\cal V}$ has {\it definable factor congruences} if and only if factor congruences can be defined by a first-order formula $\Phi $ having {\it central elements} as parameters. We prove that if $\Phi $ can be chosen to be existential, then factor congruences in every algebra of ${\cal V}$ are compact.

AMS Subject Classification (1991): 08B05, 03C40

Keyword(s): central element, compact congruence, semidegenerate variety, factor congruences

Received October 7, 2008, and in revised form May 26, 2009. (Registered under 55/2010.)