Textbook in PDF format

By a finite algebra we mean a finite set of elements together with a (possibly infinite) set of operations acting on this set of elements. This concept includes finite groups and rings and many other algebraic systems of interest in mathematics. Excluded are finite systems with infinitary operations, and those having "partial operations" (operations defined for some, but not all, n-tuples of elements). By a locally finite variety we mean a class of algebras of one type, closed under the formation of homomorphic images, subalgebras, and direct products, whose finitely generated algebras are finite.
The main discovery presented in this book is that the lattice of congruences of a finite algebra determines very deeply the structure of that algebra. Our 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. We use the theory to derive many new results that will be of interest not only to universal algebraists, but to other algebraists as well.
Basic concepts and notation.
Tight lattices.
Tame quotients.
Abelian and solvable algebras.
The structure of minimal algebras.
The types of tame quotients.
Labeled congruence lattices.
Solvability and semi-distributivity.
Congruence modular varieties.
Mal'cev classification and omitting types.
Residually small varieties.
Decidable varieties.
Free spectra.
Tame algebras and E-minimal algebras.
Simple algebras in varieties.
Problems (17).
An appendix added in July, 1996
Bibliography (85 Publ).
Added in July, 1996
Index to Terms.
Index of Notation