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Normal Bases in Galois Extensions of Number Fields

Published online by Cambridge University Press:  22 January 2016

S. Ullom
S. Ullom*
Affiliation:
University of Maryland, College Park, Maryland
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The notion of module together with many other concepts in abstract algebra we owe to Dedekind [2]. He recognized that the ring of integers OK of a number field was a free Z-module. When the extension K/F is Galois, it is known that K has an algebraic normal basis over F. A fractional ideal of K is a Galois module if and only if it is an ambiguous ideal. Hilbert [4, §§105-112] used the existence of a normal basis for certain rings of integers to develop the theory of root numbers — their decomposition already having been studied by Kummer.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 34 , March 1969 , pp. 153 - 167
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

References

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