Abstract
In a semiprime ring, von Neumann regular elements are determined by their inner inverses. In particular, for elements a, b of a von Neumann regular ring R, a = b if and only if I(a) = I(b), where I(x) denotes the set of inner inverses of x is an element of R. We also prove that, in a semiprime ring, the same is true for reflexive inverses.