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The discriminants of relative extensions and the existence of integral bases

Published online by Cambridge University Press:  26 February 2010

A. Fröhlich
A. Fröhlich
Affiliation:
King's College, London, W.C.2.
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Extract

Let Κ be a finite number field and let ο be the ring of algebraic integers in Κ. The algebraic integers in a finite extension field Λ of Κ form a ring . We shall be concerned here with the structure of such rings , viewed as modules over ο. It will be useful to begin with a brief discussion of a new concept of the discriminant of Λ/Κ, introduced in a preceding paper [1], which will be our principal tool (see also [2]).

Type
Research Article
Information
Mathematika , Volume 7 , Issue 1 , June 1960 , pp. 15 - 22
Copyright
Copyright © University College London 1960

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References

1.FrÖhlich, A., “Discriminants of algebraic number fields”, (to appear in Math. Z.).Google Scholar
2.FrÖhlich, A. “Ideals in an extension field as modules over the algebraic integers in a finite number field”, (to appear in Math. Z.).Google Scholar
3.Mann, H. B., “On integral bases”, Proc. Amer. Math. Soc., 9 (1958), 167–173.CrossRefGoogle Scholar