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.)
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