Journal of Commutative Algebra

Jaffard families and localizations of star operations

Dario Spirito

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Abstract

We generalize the concept of localization of a star operation to flat overrings; subsequently, we investigate the possibility of representing the set $\mathrm {Star}(R)$ of star operations on $R$ as the product of $\mathrm {Star}(T)$, as $T$ ranges over a family of overrings of $R$ with special properties. We then apply this method to study the set of star operations on a Prufer domain $R$, in particular the set of stable star operations and the star-class groups of $R$.

Article information

Source
J. Commut. Algebra, Volume 11, Number 2 (2019), 265-300.

Dates
First available in Project Euclid: 24 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.jca/1561363361

Digital Object Identifier
doi:10.1216/JCA-2019-11-2-265

Mathematical Reviews number (MathSciNet)
MR3973140

Zentralblatt MATH identifier
07080078

Subjects
Primary: 13A15: Ideals; multiplicative ideal theory
Secondary: 13C20: Class groups [See also 11R29] 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13F30: Valuation rings [See also 13A18] 13G05: Integral domains

Keywords
Star operations overrings Jaffard families Prufer domains class group

Citation

Spirito, Dario. Jaffard families and localizations of star operations. J. Commut. Algebra 11 (2019), no. 2, 265--300. doi:10.1216/JCA-2019-11-2-265. https://projecteuclid.org/euclid.jca/1561363361


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