Definition:Field Negative

Definition

Let $\struct {F, +, \times}$ be a field whose zero is $0_F$.

Let $x \in F$.

The inverse of $x$ with respect to the addition operation $+$ in the additive group $\struct {F, +}$ of $F$ is referred to as the (field) negative of $x$ and is denoted $-x$.

That is, the (field) negative of $x$ is the element $-x$ of $F$ such that:

$x + \paren {-x} = 0_F$