Unit

Definition

An element \(a\) of a ring with identity \(R\) is called a unit if it has a multiplicative inverse. That is, there exists a \(b \in R\) such that:

\[ ab = ba = 1.\]

The group of units is denoted by \(R^\ast\).

Note also that if \(R\) is a subring of \(S\), then the set of units of \(R\) is a subgroup of the set of units of \(S\).