  We introduce the finitistic extension degree of a ring and investigate rings
for which it is finite. The Auslander-Reiten Conjecture is proved for rings of
finite finitistic extension degree and these rings are also shown to have
finite finitistic dimension. We apply these results to better understand a gen-
eralized version of the Auslander-Reiten Condition for Gorenstein rings. We
also record how the finitistic extension degree behaves with respect to many
change of ring procedures that arise frequently in the commutative setting.
