  Let $X$ be a finitely generated left module over a left artinian ring $R$,
and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where
$l_i$ is the length of the $i$-th term of the minimal projective resolution of
$X$. We introduce a preorder relation $\le$ on the set $\{p(X)\}$ and
characterize the elementary finite-dimensional algebras $\Lambda$ with the
following property. Let $S$ be a simple $\Lambda$-module, and let $T$ be a
finitely generated module over an arbitrary left artinian ring $R$. If the
projective dimension of $S$ does not exceed the projective dimension of $T$,
then $p(S)\le p(T)$. We characterize the indicated algebras by quivers with
relations.
