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Winter 2020 The sets of star and semistar operations on semilocal Prüfer domains
Dario Spirito
J. Commut. Algebra 12(4): 581-602 (Winter 2020). DOI: 10.1216/jca.2020.12.581

Abstract

We study the sets of semistar and star operations on a semilocal Prüfer domain, with an emphasis on which properties of the domain are enough to determine them. In particular, we show that these sets depend chiefly on the properties of the spectrum and of some localizations of the domain; we also show that, if the domain is h-local, the number of semistar operations grows as a polynomial in the number of semistar operations of its localizations.

Citation

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Dario Spirito. "The sets of star and semistar operations on semilocal Prüfer domains." J. Commut. Algebra 12 (4) 581 - 602, Winter 2020. https://doi.org/10.1216/jca.2020.12.581

Information

Received: 25 July 2017; Revised: 2 March 2018; Accepted: 17 March 2018; Published: Winter 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194943
Digital Object Identifier: 10.1216/jca.2020.12.581

Subjects:
Primary: 13A15 , 13A18
Secondary: 13F05 , 13G05

Keywords: homeomorphically irreducible trees , Jaffard families , Prüfer domains , semistar operations , Star operations

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 4 • Winter 2020
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