  Let A be an Artin algebra and e an idempotent in A. It is an interesting
topic to compare the homological dimension of the algebras A,A/AeA and eAe. For
example, in [2], the relation among the global dimension of these algebras is
discussed under the condition that AeA is a strongly idempotent ideal.
Motivated by this, we try to compare the finitistic dimension of these algebras
under certain homological conditions on AeA. In particular, under the condition
that AeA is a strongly idempotent ideal with finite projective dimension, we
prove that if the finitistic projective (or injective) dimension of eAe and
A/AeA are finite, then the finitistic projective (or injective) dimension of A
is finite. This is a generalized version of the main result in [1].
