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Abstract
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For a Dedekind domain
,
let
be the set
of ideals of
that are the radical of a principal ideal. We show that, if
and
are Dedekind domains and there is an order isomorphism between
and
, then the rank of
the class groups of
and
is
the same.
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Keywords
Dedekind domain, class group, radical ideals, principal
ideals
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Mathematical Subject Classification
Primary: 13C20, 13F05
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Milestones
Received: 26 November 2020
Revised: 30 April 2021
Accepted: 16 July 2021
Published: 15 October 2021
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