What does this research mean for the field?

Transfer Krull orders in Dedekind domains with torsion class group share the same arithmetic properties as the associated Dedekind domain, except in a specific case. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To characterize which orders in Dedekind domains permit a transfer homomorphism to a monoid of zero-sum sequences under specified conditions.

March 13, 2026Open Access

A Characterization of Transfer Krull Orders in Dedekind Domains with Torsion Class Group

Key Points

To characterize which orders in Dedekind domains permit a transfer homomorphism to a monoid of zero-sum sequences under specified conditions.
Defined natural conditions for orders in Dedekind domains.
Analyzed the inclusion map as a transfer homomorphism.
Explored specific cases that violate the general case.
Identified conditions under which orders allow a transfer homomorphism.
Established that inclusion maps generally act as transfer homomorphisms, except in one case.
Showed that not all orders in Dedekind domains maintain the same arithmetic properties.

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.

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Balint Rago

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Canadian Mathematical Bulletin

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A Characterization of Transfer Krull Orders in Dedekind Domains with Torsion Class Group

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