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 D0 are Dedekind domains and there is an order isomorphism between P.D/ and P.D0/, then the rank of the class groups of D and D0 is the same.
Radicals Of Principal Ideals And The Class Group Of A Dedekind Domain
Spirito D.
2021-01-01
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 D0 are Dedekind domains and there is an order isomorphism between P.D/ and P.D0/, then the rank of the class groups of D and D0 is the same.File in questo prodotto:
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