Chapter 7

Maltsev Varieties

In this chapter we drop our assumption of congruence-distributivity, but retain congruence-permutability. Structures now will be much more group-like. We lose the power of Jónsson’s lemma, so the analysis of subdirectly irreducible algebras becomes more delicate. The study of the congruence lattices of products becomes essential. One might say that the central goal of this chapter is an understanding of skew congruences.

7.1 Directly representable varieties

Any conception of “highly structured variety” should surely include the varieties of Boolean algebras and Abelian groups. Among their attributes, the finite algebras in each of these varieties decompose nicely. In fact:

  • every finite Boolean algebra is a ...

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.