Let be a ring with multiplicative identity . We say that is an unit (or unital) if divides (denoted ). That is, there exists an such that .

Notice that will be the multiplicative inverse (in the ring) of , so we can characterize the units as those elements of the ring having multiplicative inverses.

In the special case that is the ring of integers of an algebraic number field , the units of are sometimes called the algebraic units of (and also the units of ). They are determined by Dirichlet's unit theorem.