Normal Bases in Galois Extensions of Number Fields
- 1 March 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 34, 153-167
- https://doi.org/10.1017/s0027763000024521
Abstract
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.Keywords
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