Commutator Theory in Universal Algebra

Several important concepts in universal algebra will be introduced. These include Omega-algebras, terms and term functions, congruences, and polynomial equivalence of algebras. The group-theoretic notions of an Abelian structure and of the center will be generalized to arbitrary Omega-algebras. Finally, commutators and centralizers of congruences will be defined and some of their properties proved. All of this well lead up to a proof of a nice classification theorem for Abelian structures in varieties with commutative congruences next week.