Congruence relations in direct products
Grant A. Fraser, Alfred Horn · Proceedings of the American Mathematical Society · 1970
This paper studies conditions under which every congruence relation θ \theta in a direct product A × B A \times B of algebras is of the form θ 1 × θ 2 {\theta _1} \times {\theta _2} , where θ 1 {\theta _1} and θ 2 {\theta _2} are congruence relations in A A and B B respectively. It is shown that for any equational class K K , every such θ \theta in every A × B A \times B in K K has this property if and only if K K satisfies certain identities.