Definition Unital ring ? Definition Unital ring ? Solution A ring with a multiplicative identity: an element 1 such that 1x=x=x1 for all elements x of the ring.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 uv = vu = 1R, where 1R is the multiplicative identity.the existence of such an identity is taken as part of the definition of a ring.The existence of such an identity is taken as part of the definition of a ring..