Congruence Relations in Direct Products

This paper studies conditions under which every congruence relation in a direct product <!-- MATH $A \times B$ --> of algebras is of the form <!-- MATH ${\theta _1} \times {\theta _2}$ --> , where <!-- MATH ${\theta _1}$ --> and <!-- MATH ${\theta _2}$ --> are congruence relations in and respectively. It is shown that for any equational class , every such in every <!-- MATH $A \times B$ --> in has this property if and only if satisfies certain identities.