Section Ring.
Variable R : ringType.
Definition cyclotomic (z : R) n :=
\prod_(k < n | coprime k n) ('X - (z ^+ k)%:P).
End Ring.

Lemma separable_Xn_sub_1 (R : idomainType) n :
n%:R != 0 :> R -> @separable_poly R ('X^n - 1).