Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T12:10:22.066Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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