A note on congruences
F. M. Sioson · Proceedings of the Japan Academy Series A Mathematical Sciences · 1967
The object of this note is to give necessary and sufficient conditions when a collection of disjoint non-empty subsets constitute equivalence classes of a congruence (relation) of a universal algebra.This extends previous results by M. Teissier 4 and G. B. Preston Let A-(A, O) be a universal algebra with operations O-{o1 I}.Let v be the semigroup with identity of functions generated under composition by all unary functions of the forms o(z, , -.-, a_),