Congruence classes in universal algebra. (English) Zbl 1014.08001

Chajda, Ivan; Eigenthaler, Günther; Länger, Helmut

Research and Exposition in Mathematics. 26. Lemgo: Heldermann Verlag. x, 217 p. (2003).

The book provides a collection of recent results dealing with congruence relations and congruence classes. Important statements concerning congruences and congruence classes, as well as connections to subalgebras and ideals are presented in the text.
Areas featured in the book are: congruence conditions, congruence classes and subalgebras, extension properties of congruences and their classes, regularity and its modifications, coherence and its modifications, characterizations of congruence classes, ideals in universal algebras, directly decomposable congruence classes, one-block congruences.
The book gives an excellent introduction and survey of this part of universal algebra.

Reviewer: Jaromír Duda (Brno)

MSC:

08-02	Research exposition (monographs, survey articles) pertaining to general algebraic systems
08A30	Subalgebras, congruence relations
08A05	Structure theory of algebraic structures
08B05	Equational logic, Mal’tsev conditions
08B10	Congruence modularity, congruence distributivity
08A40	Operations and polynomials in algebraic structures, primal algebras

Keywords:

variety; Mal’tsev condition; congruence relations; congruence classes; subalgebras; ideals; coherence