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ON NUMBER FIELDS WITHOUT A UNIT PRIMITIVE ELEMENT

  • T. ZAÏMI (a1), M. J. BERTIN (a2) and A. M. ALJOUIEE (a3)
Abstract

We characterise number fields without a unit primitive element, and we exhibit some families of such fields with low degree. Also, we prove that a noncyclotomic totally complex number field $K$ , with degree $2d$ where $d$ is odd, and having a unit primitive element, can be generated by a reciprocal integer if and only if $K$ is not CM and the Galois group of the normal closure of $K$ is contained in the hyperoctahedral group $B_{d}$ .

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Corresponding author
marie-jose.bertin@imj-prg.fr
References
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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