Two classes of number fields with a non-principal Euclidean ideal

Catherine Hsu

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

This paper introduces two classes of totally real quartic number fields, one of biquadratic extensions and one of cyclic extensions, each of which has a non-principal Euclidean ideal. It generalizes techniques of Graves used to prove that the number field Q(√2,√35) has a non-principal Euclidean ideal.
Original languageEnglish
Pages (from-to)1123-1136
Number of pages13
JournalInternational Journal of Number Theory
Volume12
Issue number4
DOIs
Publication statusPublished - 28 Sep 2015

Keywords

  • Euclidean ideals
  • Hilbert class field
  • cyclic class group
  • biquadratic quartic field
  • cyclic quartic field

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