Is the following an isomorphism:
$ \mathbb {Q}(\zeta_m)/ \mathbb{Q} \cong \mathbb{Z}[X]/ X^m -1 $
Where $ \mathbb {Q}(\zeta_m)/ \mathbb{Q}$ is a field extension created by adjoining $\zeta_m$, an m'th root of unity, to the rationals ?
How about the following:
$ \mathbb{Q}(\zeta_m)/\mathbb{Q} \cong \mathbb{Z}[X]/ \Phi_m(X)$ where $\Phi_m(X)$ is the m'th cyclotomic polynomial ?