# Unit (Ring)

Definition : Let $R$ be a ring. $u \in R$ is a unit if there exist $v \in R$ such that $u*v = 1_R$ where $1_R$ is the multiplicative identity.

Let $R$ be a Ring. An element $u \in R$ is a unit if there exists inverse element $v \in R$ so that $u*v = 1_R$; $1_R$ is the multiplicative identity of $R$. For example in the integers only $1$ and $-1$ are units since these are the only numbers that can create a product of $1$. If a Ring as a unit it will not have zero divisors.