Semistar dimension of polynomial rings and Prüfer-like domains

2008/08/09 by Parviz Sahandi, Sahandi, Parviz
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.AC #msc:13A15 #msc:13C15 #msc:13G05

paper · pdf · doi:10.48550/arxiv.0808.1331

12 pages

arxiv created 2010/02/20 · arxiv updated 2010/02/26

Abstract

Let D 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-Prüfer 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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