(1,2)-Engel-type Lie ring

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

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