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Paper   IPM / M / 8984
School of Mathematics
  Title:   Universally catenarian integral domains, strong S-domains and semistar operations
  Author(s):  P. Sahandi
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  38
  Year:  2010
  Pages:   673-683
  Supported by:  IPM
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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