Def. The units in a Unital ring $R$ are elements with a multiplicative inverse. That is an element $a \in R$ is called an unit, if $\exists b \in$, s.t. $ab=ba =1$. $b$ will be unique, denote it $a^{-1}$.

The set of units in $R$ is denoted $R^*$.

Proposition. Let R be a ring with 1, then $R^*$ is a Group, called the Multiplicative group