Characteristic ideal of a Lie ring

Definition
A subset of a Lie ring is termed a characteristic ideal if it satisfies both the following conditions:


 * 1) It is a characteristic Lie subring, i.e., it is invariant under all the automorphisms of the whole Lie ring.
 * 2) It is an ideal of the Lie ring, i.e., it is invariant under all the inner derivations of the whole Lie ring.