ACTA issues

Existentially definable factor congruences

Pedro Sánchez Terraf

Acta Sci. Math. (Szeged) 76:1-2(2010), 49-53
55/2010

 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.)