Homomorph-containing subgroup of additive group of Lie ring is self-derivation-invariant and homomorph-containing

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Suppose L is a Lie ring, and A is a subgroup of the additive group of L such that A is a homomorph-containing subgroup of L. Then, the following three conditions hold:

  1. A is a Lie subring of L.
  2. A is a self-derivation-invariant Lie subring of L.
  3. A is a homomorph-containing Lie subring of L.

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