Ideal core of a Lie subring

ANALOGY: This is an analogue in Lie rings of a term encountered in group. That term is: normal core.
View other analogues of normal core

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 inner derivations of $L$.

Related notions

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