End FieldRingMap.
Section FieldMap.
Variable rR : idomainType.
Variable f : {rmorphism F -> rR}.
Local Notation "p ^f" := (map_poly f p) : ring_scope.
Implicit Type a b : {poly F}.

Lemma coprimepP (p q : {poly F}):
reflect (forall x, root p x -> q.[x] != 0) (coprimep p q).