%0 Journal Article %T Semistar dimension of polynomial rings and Prufer-like domains %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Sahandi, P. %D 2011 %\ 09/15/2011 %V 37 %N No. 3 %P 217-233 %! Semistar dimension of polynomial rings and Prufer-like domains %K Semistar operation %K Krull dimension %K strong S-domain %K Jaffard domain %K quasi-Pr"{u}fer domain %K UM$t$ domain %R %X 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. %U http://bims.iranjournals.ir/article_361_6dbe9e5fa7817562fab715a62353d061.pdf