Chapter 6
Arithmetical Varieties
The previous chapter was concerned with the lattice-theoretic property of distributivity, and the influence it has on the structure of a variety. However, there is another property of a congruence lattice — permutability — that plays an important role. In this chapter, we study the combination of congruence-distributivity and -permutability and its effect on the clone of term operations.
6.1 Large clones
Universal algebra is at least partly a search for objects with an especially rich structure. Of course “rich structure” is in the eye of the beholder. Perhaps the congruence lattice has some important property or the identities that hold in the algebra are of a special form. In this section we consider ...
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