Monatshefte für Mathematik

, Volume 94, Issue 2, pp 125–132

On cyclic biquadratic fields related to a problem of Hasse

  • Toru Nakahara
Article

DOI: 10.1007/BF01301930

Cite this article as:
Nakahara, T. Monatshefte für Mathematik (1982) 94: 125. doi:10.1007/BF01301930

Abstract

In this note we shall prove that there exist infinitely many cyclic biquadratic fieldsK whose integral bases are neither {1, α, α2, β} nor {1, α, β, α3) for any numbers α, β inK. Next, we shall construct infinitely many cyclic biquadratic fieldsK which have the index 1, but still have not the integral basis {1, α, α2, α3) for every α inK. Finally we shall give a class of biquadratic fields for a problem of Hasse concerning an integral basis.

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Toru Nakahara
    • 1
  1. 1.Department of Mathematics Faculty of Science and EngineeringSaga UniversitySagaJapan