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 kHomP {K V f} :
reflect [/\ {in V &, forall x y, f (x * y) = f x * f y}
& {in K, forall x, f x = x}]
(kHom K V f).