let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on
it. we define the semistar dimension (inequality) formula and
discover their relations with $star$-universally catenarian
domains and $star$-stably strong s-domains. as an application, we
give new characterizations of $star$-quasi-pr"{u}fer domains
and um$t$ domains in terms of dimension ine...
