Definition:Zero Element

Definition
Let $\struct {S, \circ}$ be an algebraic structure.

Zero
An element $z \in S$ is called a two-sided zero element (or simply zero element or zero) it is both a left zero and a right zero:
 * $\forall x \in S: x \circ z = z = z \circ x$

Also see

 * Definition:Identity Element


 * Zero Element is Unique