Affine complete varieties are congruence distributive
An algebra is affine complete if every function on \(A\) compatible with Con\(A\) is a polynomial over \(A\). A variety \(V\) is affine complete if all its members are. It is shown that every affine complete variety is congruence distributive and residually finite and a useful characterization of all arithmetical affine complete varieties of countable type is given. It is shown that affine complete varieties with finite residual bound have enough injectives and an example of an affine complete variety without finite residual bound is constructed. There are also several results concerning residually finite varieties whose finite members are congruence distributive.
scientific article; zbMATH DE number 1407080