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