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

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.

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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

Vol. 314, No. 1, 2021

Dario Spirito

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors