Definition:Unit of Ring/Definition 1

Definition
Let $\struct {R, +, \circ}$ be a ring with unity whose unity is $1_R$.

An element $x \in R$ is a unit of $\struct {R, +, \circ}$ $x$ is invertible under $\circ$.

That is, a unit of $R$ is an element of $R$ which has an inverse.
 * $\exists y \in R: x \circ y = 1_R = y \circ x$

Also see

 * Equivalence of Definitions of Unit of Ring