Ideal core of a Lie subring

Definition
Let $$L$$ be a Lie ring and $$A$$ be a Lie subring of $$L$$. The ideal core of $$A$$ is defined in the following equivalent ways:


 * 1) It is the largest ideal of $$L$$ that is contained in $$A$$.
 * 2) it is the intersection of $$A$$ and all subgroups of $$L$$ of the form $$(d_1 \circ d_2 \circ \dots \circ d_r)^{-1}(A)$$ where the $$d_i$$ are defining ingredient::inner derivations of $$L$$.

Other core operators for Lie rings

 * Derivation-invariant core of a Lie subring

Other operators

 * Ideal closure of a Lie subring
 * Idealizer of a Lie subring