Integers form Commutative Ring with Unity

Theorem
The integers $\left({\Z, +, \times}\right)$ form a commutative ring with unity under addition and multiplication.

Proof
We have that:


 * $\left({\Z, +, \times}\right)$ form a commutative ring.


 * $\left({\Z, +, \times}\right)$ has a unity, and the unity is $1$.