Unit (ring theory)

In ring theory, a **unit** is an element of a ring that has a multiplicative inverse within that ring. More formally, let \( R \) be a ring. An element \( u \in R \) is called a unit if there exists an element \( v \in R \) such that: \[ u \cdot v = 1 \] where \( 1 \) is the multiplicative identity in the ring \( R \).