Canonical gen_rmorphism := RMorphism gen_is_rmorphism.
(* The generated field contains a root of the minimal polynomial (in some  *)
(* cases we want to use the construction solely for that purpose).         *)
Definition groot := inFA (poly_rV ('X %% pA)).

(* Specifications: *)
Lemma mxval_groot : mxval groot = A.
Lemma mxval_grootX k : mxval (groot ^+ k) = A ^+ k.
(* Plugging the extension morphism gen into the ext_repr construction   *)
(* yields a (reducible) tensored representation.                           *)
Lemma non_linear_gen_reducible :
d > 1 -> mxnonsimple (map_repr gen_rmorphism rG) 1%:M.