Semistar dimension of polynomial rings and Prufer-like domains
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Abstract:
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.
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Journal title
volume 37 issue No. 3
pages 217- 233
publication date 2011-09-15
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