Remarks on normal bases
Volume 87 / 2001
Colloquium Mathematicum 87 (2001), 79-84
MSC: Primary 11R33.
DOI: 10.4064/cm87-1-4
Abstract
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.
