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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Relative integral bases


Author: Lawrence C. Washington
Journal: Proc. Amer. Math. Soc. 56 (1976), 93-94
MSC: Primary 12A35
DOI: https://doi.org/10.1090/S0002-9939-1976-0399041-9
Erratum: Proc. Amer. Math. Soc. 70 (1978), 92.
MathSciNet review: 0399041
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Abstract: We give necessary and sufficient conditions for certain quadratic extensions of imaginary quadratic fields to have relative integral bases.


References [Enhancements On Off] (What's this?)

  • [1] E. Artin, Questions de base minimale dans la théorie des nombres algébriques, Algèbre et Théorie des Nombres., Colloques Internationaux du Centre National de la Recherche Scientifique, no. 24, Centre National de la Recherche Scientifique, Paris, 1950, pp. 19–20 (French). MR 0042450
  • [2] Genjiro Fujisaki, Some examples of number fields without relative integral bases, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 21 (1974), 93–95. MR 0345931
  • [3] Serge Lang, Algebraic number theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0282947
  • [4] Robert MacKenzie and John Scheuneman, A number field without a relative integral basis, Amer. Math. Monthly 78 (1971), 882–883. MR 0288094, https://doi.org/10.2307/2316485

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399041-9
Keywords: Relative integral bases, quadratic fields
Article copyright: © Copyright 1976 American Mathematical Society