This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.

Table of Contents

• Introduction
• Preliminary notions
• Strong term conditions
• Meet continuous congruence identities
• Rectangulation
• A theory of solvability
• Ordinary congruence identities
• Congruence meet and join semidistributivity
• Residually small varieties
• Problems
• Appendix A. Varieties with special terms
• Bibliography
• Index