If $A$ is a ring, the center of $A$ sometimes denoted $\operatorname{Z}(A)$ is the set of all elements in $A$ that commute with all other elements of $A$ That is, $$\operatorname{Z}(A) = \{ a \in A \mid ax = xa \text{} \forall x \in A \}$$

Note that $0 \in \operatorname{Z}(A)$ so the center is non-empty. If we assume that $A$ is a ring with a multiplicative unity $1$ then $1$ is in the center as well. The center of $A$ is also a subring of $A$