  Following the well-established terminology in commutative algebra, any (not
necessarily commutative) finite-dimensional local algebra $A$ with radical $J$
will be said to be short provided $J^3 = 0$. As in the commutative case, also
in general, the asymptotic behavior of the Betti numbers of modules seems to be
of interest. As we will see, there are only few possibilities for the growth of
the Betti numbers of modules. We generalize results which are known for
commutative algebras, but some of our results seem to be new also in the
commutative case.
