Remarks on normal bases, by Marcin Mazur
We prove that any Galois extension of commutative rings with normal
and abelian Galois group of odd order has a self dual normal basis. Also
show that if S/R is an unramified extension of number rings with
Galois group of odd order and $R$ is totally real then the normal
basis does not exist for S/R.
Marcin Mazur <email@example.com>