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A characterization of transfer Krull orders in Dedekind domains with Torsion class group

Part of: Arithmetic rings and other special rings Algebraic number theory: global fields General commutative ring theory

Published online by Cambridge University Press:  10 March 2026

Balint Rago Open the ORCID record for Balint Rago [Opens in a new window]
Balint Rago*
Affiliation:
University of Graz , Austria
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e-mail: balint.rago@uni-graz.at
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Abstract

We establish a characterization (under some natural conditions) of those orders in Dedekind domains which allow a transfer homomorphism to a monoid of zero-sum sequences. As a consequence, the inclusion map to the Dedekind domain is a transfer homomorphism, with the exception of a particular case. The arithmetic of Krull and Dedekind domains is well understood, and the existence of a transfer homomorphism implies that the order and the associated Dedekind domain share the same arithmetic properties. This is not the case for arbitrary orders in Dedekind domains.

Keywords

OrdersDedekind domainstransfer Krull

MSC classification

Primary: 11R27: Units and factorization 13A05: Divisibility; factorizations 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations

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Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 16
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Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported by the FWF (projects W1230 and 10.55776/DOC-183-N).

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