  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 $x\in R$. We also prove that, in a semiprime ring, the same is true
for reflexive inverses.
