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|Paper IPM / M / 8984||
Let D be an integral domain and ∗ a semistar operation stable and of finite type on it.
In this paper, we are concerned with the study of the semistar
(Krull) dimension theory of polynomial rings over D. We
introduce and investigate the notions of ∗-universally
catenarian and ∗-stably strong S-domains and prove that,
every ∗-locally finite dimensional Prüfer
∗-multiplication domain is ∗-universally catenarian,
and this implies ∗-stably strong S-domain. We also give new
characterizations of ∗-quasi-Prüfer domains introduced
recently by Chang and Fontana, in terms of these notions.
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