# Ring Negative is Unique

## Theorem

Let $\struct {R, +, \circ}$ be a ring.

Let $a \in R$.

Then the ring negative $-a$ of $a$ is unique.

## Proof

The ring negative is, by definition of a ring, the inverse element of $a$ in the additive group $\struct {R, +}$.

The result then follows from Inverse in Group is Unique.

$\blacksquare$