Ideal core of a Lie subring

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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

Other operators