End SplittingFieldFor.
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.

Lemma kHom_is_rmorphism K E f :
kHom K E f -> rmorphism (f \o vsval : subvs_of E -> L).