Definition:Product Inverse

Definition

Let $\left({R, +, \circ}\right)$ be a ring with unity.

Let $U_R$ denotes the group of units of $R$.

The inverse of $x \in U_R$ by $\circ$ is called the (ring) product inverse of $x$.

The usual means of denoting the product inverse of an element $x$ is by $x^{-1}$.

Thus it is distinguished from the additive inverse of $x$, i.e. the (ring) negative of $x$, which is usually denoted $-x$.