(* Centralizer subgroup and central homomorphisms. *)
Section CentHom.
Variable f : 'M[F]_n.

(* Specifications: *)
Lemma row_full_dom_hom : row_full (dom_hom_mx f) = centgmx rG f.
Lemma memmx_cent_envelop : (f \in 'C(E_G))%MS = centgmx rG f.
Lemma kermx_centg_module : centgmx rG f -> mxmodule (kermx f).
Lemma centgmx_hom m (U : 'M_(m, n)) : centgmx rG f -> (U <= dom_hom_mx f)%MS.
(* Schur's lemma for endomorphisms. *)
Lemma mx_Schur :
mx_irreducible -> forall f, centgmx rG f -> f != 0 -> f \in unitmx.