\begin{definition}[Definition:Additive Inverse/Ring]
Let $\struct {R, +, \circ}$ be a ring whose ring addition operation is $+$.
Let $a \in R$ be any arbitrary element of $R$.
The '''additive inverse''' of $a$ is its inverse under ring addition, denoted $-a$:
:$a + \paren {-a} = 0_R$
where $0_R$ is the zero of $R$.
\end{definition}