Negative of Ring Negative

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Theorem

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

Let $a \in R$ and let $-a$ be the ring negative of $a$.


Then:

$-\paren {-a} = a$


Proof

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

The result then follows from Inverse of Group Inverse.

$\blacksquare$


Sources