be a variety of associative algebras generated by an algebra with 1 over a field of characteristic zero. This paper is devoted to the classification of the varieties
that are minimal of polynomial growth (i.e., their sequence of codimensions grows like
, but any proper subvariety grows like
). These varieties are the building blocks of general varieties of polynomial growth.
It turns out that for
there are only a finite number of varieties of polynomial growth
, but for each
, the number of minimal varieties is at least
$\left| F \right|$
, the cardinality of the base field, and we give a recipe for their construction.