Section kHom.
Variables (F : fieldType) (L : fieldExtType F).
Implicit Types (U V : {vspace L}) (K E : {subfield L}) (f g : 'End(L)).
Definition kHom U V f := ahom_in V f && (U <= fixedSpace f)%VS.
Definition kHom_rmorphism K E f homKEf :=
RMorphism (@kHom_is_rmorphism K E f homKEf).

Lemma kHom_root_id K E f p x :
(K <= E)%VS -> kHom K E f -> p \is a polyOver K -> x \in E -> root p x ->
root p (f x).