In mathematics, an invertible element or a unit in a (unital) ring R is any element u that has an inverse element in the multiplicative monoid of R, i.e. an element v such that

The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation. It never contains the element 0 (except in the case of the zero ring), and is therefore not closed under addition; its complement however might be a group under addition, which happens if and only if the ring is a local ring.