Vol. 314, No. 1, 2021

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Radicals of principal ideals and the class group of a Dedekind domain

Dario Spirito

Vol. 314 (2021), No. 1, 219–231
Abstract

For a Dedekind domain D, let 𝒫(D) be the set of ideals of D that are the radical of a principal ideal. We show that, if D and D are Dedekind domains and there is an order isomorphism between 𝒫(D) and 𝒫(D), then the rank of the class groups of D and D is the same.

Keywords
Dedekind domain, class group, radical ideals, principal ideals
Mathematical Subject Classification
Primary: 13C20, 13F05
Milestones
Received: 26 November 2020
Revised: 30 April 2021
Accepted: 16 July 2021
Published: 15 October 2021
Authors
Dario Spirito
Dipartimento di Matematica
Università di Padova
Padova
Italy
Dipartimento di Matematica e Fisica
Università degli Studi “Roma Tre”
Roma
Italy