Semistar dimension of polynomial rings and Pr\"{u} fer-like domains
P Sahandi - arXiv preprint arXiv:0808.1331, 2008 - arxiv.org
arXiv preprint arXiv:0808.1331, 2008•arxiv.org
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 …
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 …
Let be an integral domain and 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 -universally catenarian domains and -stably strong S-domains. As an application we give new characterizations of -quasi-Pr\"{u}fer domains and UM 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.
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