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 edivp_map a b :
edivp a^f b^f = (0%N, (a %/ b)^f, (a %% b)^f).