Ring Negative is Unique

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Theorem

Let $\left({R, +, \circ}\right)$ 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 $\left({R, +}\right)$.

The result then follows from Inverse in Group is Unique.

$\blacksquare$


Sources