  Let $\Lambda$ be an artin algebra, and $\mathcal{V}$ a subset of all simple
modules in $\mod\Lambda$. Suppose that $\Lambda/\rad \Lambda$ has finite syzygy
type, then the derived dimension of $\Lambda$ is at most
$\ell\ell^{t_{\mathcal{V}}}(\Lambda_{\Lambda})+\pd\mathcal{V}.$ In particular,
if the global dimension of $\Lambda$ is finite, then the derived dimension of
$\Lambda$ is at most
$\ell\ell^{t_{\mathcal{V}}}(\Lambda_{\Lambda})+\pd\mathcal{V}.$ This
generalized the famous result which state that the derived dimension of
$\Lambda$ is less than or equal to the global dimension of $\Lambda$.
