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A remark on relative integral bases for infinite extensions of finite number fields

Published online by Cambridge University Press:  26 February 2010

C. U. Jensen
C. U. Jensen
Affiliation:
University of Copenhagen, Denmark
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Extract

Let K be a finite algebraic extension of the rational number field Q, and let R denote the ring of algebraic integers in K. The algebraic integers in a finite extension field of K form a ring which may be considered as a module over R. The structure of these modules has been entirely determined in Fröhlich [2], where, in particular, necessary and sufficient conditions have been established deciding when such a module will be a free R-module.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 64 - 66
Copyright
Copyright © University College London 1964

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References

1.Cartan, H. and Eilenberg, S., Homological algebra (Princeton University Press, 1956).Google Scholar
2.Fröhlich, A., “The discriminant of relative extensions and the existence of integral bases”, Mathematiha, 7 (1960), 15–22.CrossRefGoogle Scholar
3.Kaplansky, I., “Modules over Dedekind rings and valuation rings”, Trans. American Math. Soc., 72 (1952), 327–340.CrossRefGoogle Scholar
4.Zariski, O. and Samuel, P., Commutative algebra, vol. I (Van Nostrand Company, 1958).Google Scholar