Semistar dimension of polynomial rings and Prufer-like domains

Document Type : Research Paper



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 inequality formula (and
the notions of universally catenarian domain, stably strong
S-domain, strong S-domain, and Jaffard domain). We also extend
Arnold's formula to the setting of semistar operations.