  In this work, the lattice of varieties of semigroups and the lattice of
varieties of I-semigroups (a common setting for both the variety of completely
regular semigroups and the variety of inverse semigroups) are studied with
respect to the following concepts: a variety V of (I-)semigroups is said to be
locally K-finite, where K stands for any of the five Green's relations, if
every finitely generated semigroup from V has only finitely many (distinct)
K-classes.
