Semistar dimension of polynomial rings and Prufer-like domains

چکیده مقاله

Let $D$ be an integral domain and $\star$ a semistar operation stable and of finite type on
it. In this paper 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 inequality formula (and the notions of universally
catenarian domain, stably strong S-domain, strong S-domain, and
Jaffard domains). We also extend Arnold's formula to the setting of
semistar operations.