Part II
Selected Topics
Introduction to Part II
We have thus far discussed several properties that a variety may or may not possess. For example, a variety V is called locally finite if every finitely generated member is finite, and V is finitely generated if it is of the form V(K) where K is a finite set of finite algebras. We have also seen some implications that hold among these properties. In Theorem 3.49 we proved that every finitely generated variety is locally finite.
This aspect of universal algebra is the primary focus of Part II. More precisely, the central theme is the structure of congruence lattices. More than any other, this has proved to be a key organizing principle in the study of varieties.
Recall that an algebra is called ...
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