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Paper   IPM / M / 11336
School of Mathematics
  Title:   Semistar dimension of polynomial rings and Prufer-Like domains
  Author(s):  P. Sahandi
  Status:   Published
  Journal: Bull. Iranian Math. Soc.
  Vol.:  37
  Year:  2011
  Pages:   217-233
  Supported by:  IPM
Let D be an integral domain and * a semis tar 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-Priifer domains and UMt 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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