Section Ring.
Context {R:Type}`{Rr:Ring R}.
(* Powers *)
Definition id_phi_N (x:N) : N := x.

(** Identity is a morphism *)
(* Instance IDmorph : Ring_morphism _ _ _  (fun x => x). *)
(** rings are almost rings*)
Lemma ring_mul_0_l : forall  x, 0 * x == 0.