Section IntegralOverRing.
Definition integralOver (R K : ringType) (RtoK : R -> K) (z : K) :=
exists2 p, p \is monic & root (map_poly RtoK p) z.
Definition integralRange R K RtoK := forall z, @integralOver R K RtoK z.
Variables (B R K : ringType) (BtoR : B -> R) (RtoK : {rmorphism R -> K}).

(* Specifications: *)
Lemma integral_rmorph x :
integralOver BtoR x -> integralOver (RtoK \o BtoR) (RtoK x).