# Unit (ring theory)

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In ring theory we say that an element $u$ of a ring $R$ is a unit if it has an inverse in $R$, that is, if there is another element $v\in R$ such that $uv=vu=1$.

It is easy to show that the set of units $U(R)$ of a ring forms a group under multiplication. This group is known as the group of units of $R$.