∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B), (RingHom.ker f).IsTwoSided