Units in Rings

Given a ring $(R, +, \cdot)$ with $1_{R}$ , $u \in R$ is a (multiplicative) unit if there exists $v \in R$ , such that $uv = vu = 1_{R}$ .

$R^{\times} = {u \in R ∣ u is a unit}$ , $(R^{\times}, \cdot)$ is a group (where $\cdot$ is the multiplication in $R$ ).

My Math Notes