Structure of Finite Algebras

The main discovery presented here is that the lattice of congruences of a finite algebra is deeply connected to the structure of that algebra. The theory reveals a sharp division of locally finite varieties of algebras into six interesting new families, each of which is characterized by the behavior of congruences in the algebras. The authors use the theory to derive many new results that will be of interest not only to universal algebraists, but to other algebraists as well.
The authors begin with a straightforward and complete development of basic tame congruence theory, a topic that offers great promise for a wide variety of investigations. They then move beyond the consideration of individual algebras to a study of locally finite varieties. A list of open problems closes the work.