We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-4,
author = {Marcin Mazur},
title = {Remarks on normal bases},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {79-84},
zbl = {0964.11050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-4}
}
Marcin Mazur. Remarks on normal bases. Colloquium Mathematicae, Tome 89 (2001) pp. 79-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-4/