Commutator Theory and Abelian Algebras

Abstract

This is the first draft of a set of lecture notes developed for one-half of a seminar on two approaches to the notion of "Abelian", namely those of universal algebra, and of category theory. The half pertaining to the universal-algebraic perspective is covered here. All material has been adapted from the following sources: 1. Commutator Theory for Congruence Modular Varieties, by Ralph Freese and Ralph McKenzie. 2. Geometrical Methods in Congruence Modular Algebras, by H. Peter Gumm 3. Congruence Modular Varieties: Commutator Theory and Its Uses, by Ralph McKenzie and John Snow