Subrings of Integers are Sets of Integer Multiples/Examples/Even Integers

Theorem
Let $2 \Z$ be the set of even integers.

Then $\struct {2 \Z, +, \times}$ is a subring of $\struct {\Z, +, \times}$.

Proof
From Subrings of Integers are Sets of Integer Multiples, a ring of the form $\struct {n \Z, +, \times}$ is a subring of $\struct {\Z, +, \times}$ when $n \ge 1$.

$\struct {2 \Z, +, \times}$ is such an example.