(2,1)-Engel-type Lie ring

Definition
A (2,1)-Engel-type Lie ring is a Lie ring of given right-normed Engel-type signature $$(2,1)$$. Explicitly, a Lie ring $$L$$ is a (2,1)-Engel-type Lie ring if it satisfies:

$$[x,[x,[y,z]]] = 0 \ \forall \ x,y,z \in L$$