Perfect direct factor implies derivation-invariant

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This article gives the statement and possibly, proof, of an implication relation between two Lie subring properties. That is, it states that every Lie subring satisfying the first Lie subring property (i.e., perfect direct factor of a Lie ring) must also satisfy the second Lie subring property (i.e., derivation-invariant Lie subring)
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Statement

Any perfect direct factor of a Lie ring is a derivation-invariant Lie subring. In particular, it is a Derivation-invariant direct factor (?) of the whole ring.

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