# Definition:Ring Negative

## Definition

Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.

Let $x \in R$.

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

That is, the (ring) negative of $x$ is the element $-x$ of $R$ such that:

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