# Subring of Integers is Ideal

## Theorem

Let $\struct {\Z, +}$ be the additive group of integers.

Every subring of $\struct {\Z, +, \times}$ is an ideal of the ring $\struct {\Z, +, \times}$.

## Proof

Follows directly from:

Subrings of Integers are Sets of Integer Multiples

and:

Subgroup of Integers is Ideal.

$\blacksquare$