### Remarks on normal bases, by Marcin Mazur

We prove that any Galois extension of commutative rings with normal
basis
and abelian Galois group of odd order has a self dual normal basis. Also
we
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 <mazur@math.uchicago.edu>