Chapter 8

Finite Algebras and Locally Finite Varieties

Throughout this text we have considered numerous results about finite algebras. So it might seem strange to conclude with a chapter devoted to finite algebras. However, our emphasis here is different. In the previous chapters we studied the influence of the global properties of the congruence lattices (distributivity, permutability, etc.) on the behavior of the algebras. In this chapter we shall investigate the interplay between the polynomial operations and the individual congruences (actually, pairs of congruences) of an algebra and what it tells us about structure.

One prototype of this approach is the commutator, which we studied in Sections 7.2 through 7.4. The relation “α centralizes ...

Get Universal Algebra now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.