Transfinitely valued Euclidean domains have arbitrary indecomposable order type

Chris J. Conidis, Pace P. Nielsen, Vandy Tombs

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely characterize the norm complexity of Euclidean domains. Modifying this construction, we also find a finitely valued Euclidean domain with no multiplicative integer valued norm.

Original languageEnglish
Pages (from-to)1105-1113
Number of pages9
JournalCommunications in Algebra
Volume47
Issue number3
DOIs
StatePublished - Mar 4 2019
Externally publishedYes

Funding

This work was supported by the National Security Agency [grant number H98230-16-1-0048].

Keywords

  • Euclidean domain
  • indecomposable ordinal
  • multiplicative norm
  • transfinitely valued

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