Center of a Lie ring

Definition
The center of a Lie ring $$L$$, denoted $$Z(L)$$, is defined as:

$$Z(L) = \{ x \in L \mid [x,y] = 0 \ \forall \ y \in L \}$$

The center of a Lie ring is a subring, and, in fact, is an Abelian ideal in the Lie ring.