Acta Mathematica Hungarica

, Volume 70, Issue 3, pp 185–192 | Cite as

Relative integral bases for quartic fields over quadratic subfields

  • B. K. Spearman
  • K. S. Williams


Integral Basis Quartic Field Quadratic Subfield 
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  1. [1]
    E. Artin, Questions de base minimale dans la théorie des nombres algébriques,Alg. Th. des Nombres, Coll. Internat. CNRS,24 (1950), 19–20.Google Scholar
  2. [2]
    R. H. Bird and C. J. Parry, Integral bases for bicyclic biquadratic fields over quadratic subfields,Pacific J. Math.,66 (1976), 29–36.Google Scholar
  3. [3]
    H. M. Edgar, A number field without any integral basis,Math. Mag.,52 (1979), 248–251.Google Scholar
  4. [4]
    T. Funakura, On integral bases of pure quartic fields,Math. J. Okayama Univ.,26 (1984), 27–41.Google Scholar
  5. [5]
    J. G. Huard, B. K. Spearman and K. S. Williams,Integral bases for quartic fields with quadratic subfields, Carleton University Centre for Research in Algebra and Number Theory Mathematical Research Series No. 4, June 1991, 44 pp.Google Scholar
  6. [6]
    J. G. Huard, B. K. Spearman and K. S. Williams, Integral bases for quartic fields with quadratic subfields,J. Number Theory,51 (1995), 87–102.CrossRefGoogle Scholar
  7. [7]
    J. A. Hymo and C. J. Parry, On relative integral, bases for cyclic quartic fields,J. Number Theory,34 (1990), 189–197.CrossRefGoogle Scholar
  8. [8]
    J. A. Hymo and C. J. Parry, On relative integral bases for pure quartic fields,Indian J. Pure Appl. Math.,23 (1992), 359–376.Google Scholar
  9. [9]
    R. MacKenzie and J. Scheuneman, A number field without a relative integral basis,Amer. Math. Monthly,78 (1971), 882–883.Google Scholar
  10. [10]
    M. Pohst, Berechnung unabängiger Einheiten und Klassenzahlen in total reellen biquadratischen Zahlkörpern,Computing,14 (1975), 67–78.Google Scholar
  11. [11]
    B. Schmal,Existenz von relativen ganzheitsbasen bei quartischen, insbesondere bi-quadratischen Erweiterungskörpern über quadratischen Grundkörpern (Diplomarbeit), Universität des Saarlandes (1984).Google Scholar
  12. [12]
    B. K. Spearman and K. S. Williams, Cyclic quartic fields with relative integral bases over their quadratic subfields,Proc. Amer. Matie. Soc.,103 (1988), 687–694.Google Scholar
  13. [13]
    Zhang Xianke, Cyclic quartic fields and genus theory of their subfields,J. Number Theory,18 (1984), 350–355.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • B. K. Spearman
    • 1
  • K. S. Williams
    • 2
  1. 1.Department of MathematicsOkanagan University CollegeKelownaCanada
  2. 2.Department of Mathematics and StatisticsCarleton UniversityOttawaCanada

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