Memoirs of the American Mathematical Society 2013; 169 pp; softcover Volume: 222 ISBN10: 0821883232 ISBN13: 9780821883235 List Price: US$83 Individual Members: US$49.80 Institutional Members: US$66.40 Order Code: MEMO/222/1046
 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
