Chapter 5
Congruence Distributive Varieties
In lattice theory, distributivity is the single strongest property. Distributive lattices have a relatively simple structure and often the key to the structure of an arbitrary lattice lies in isolating distributive sublattices.
It should not be too surprising then to find that algebras with distributive congruences often have nice properties. As we shall see in this chapter, varieties in which every algebra has a distributive congruence lattice lend themselves to deep analysis. The central tool is a discovery of B. Jonsson that imposes considerable structure on the subdirectly irreducible members. This allows an analysis of the subvarieties of a variety, as well as the equations satisfied by its ...
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