Uniquely Lazard-divided Lie ring

Definition
A Lazard-divided Lie ring is termed a uniquely Lazard-divided Lie ring if the underlying Lie ring structure determines all the Lazard division operations uniquely. Explicitly, this means that if the additive structure and Lie bracket are known, each of the Lazard division operations is uniquely determined.

The corresponding Lie ring property is termed uniquely Lazard-dividable Lie ring.