Localizations of integer‐valued polynomials and of their Picard group

Author:

Spirito Dario1ORCID

Affiliation:

1. Dipartimento di Scienze Matematiche Informatiche e Fisiche Università degli Studi di Udine Udine Italy

Abstract

AbstractWe prove a necessary and sufficient criterion for the ring of integer‐valued polynomials to behave well under localization. Then, we study how the Picard group of Int(D) and the quotient group behave in relation to Jaffard, weak Jaffard, and pre‐Jaffard families; in particular, we show that when T ranges in a Jaffard family of D, and study when similar isomorphisms hold when T ranges in a pre‐Jaffard family. In particular, we show that the previous isomorphism holds when D is an almost Dedekind domain such that the ring integer‐valued polynomials behave well under localization and such that the maximal space of D is scattered with respect to the inverse topology.

Publisher

Wiley

Subject

General Mathematics

Reference26 articles.

1. Remarks on generalized rings of quotients;Akiba T.;Proc. Japan Acad.,1964

2. Mori domains of integer-valued polynomials

3. Integer‐valued polynomials, Prüfer domains, and localization;Chabert J.‐L.;Proc. Amer. Math. Soc.,1993

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