∀ {R : Type u_4} [inst : CommRing R] {A : Type u_6} {C : Type u_8} {D : Type u_9} [inst_1 : Ring A] [inst_2 : Ring C]
  [inst_3 : Ring D] [inst_4 : Algebra R A] [inst_5 : Algebra R C] [inst_6 : Algebra R D] (g : C →ₐ[R] D),
  Function.Surjective ⇑g →
    RingHom.ker (Algebra.TensorProduct.map (AlgHom.id R A) g) =
      Ideal.map Algebra.TensorProduct.includeRight (RingHom.ker g)