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.
Sahandi, P. (2011). Semistar dimension of polynomial rings and Prufer-like
domains. Bulletin of the Iranian Mathematical Society, 37(No. 3), 217-233.
MLA
P. Sahandi. "Semistar dimension of polynomial rings and Prufer-like
domains". Bulletin of the Iranian Mathematical Society, 37, No. 3, 2011, 217-233.
HARVARD
Sahandi, P. (2011). 'Semistar dimension of polynomial rings and Prufer-like
domains', Bulletin of the Iranian Mathematical Society, 37(No. 3), pp. 217-233.
VANCOUVER
Sahandi, P. Semistar dimension of polynomial rings and Prufer-like
domains. Bulletin of the Iranian Mathematical Society, 2011; 37(No. 3): 217-233.
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