  It is proved that the universal degree bound for separating polynomial
invariants of a finite abelian group (in non-modular characteristic) is
strictly smaller than the universal degree bound for generators of polynomial
invariants, unless the goup is cyclic or is the direct product of $r$ even
order cyclic groups where the number of two-element direct factors is not less
than the integer part of the half of $r$. A characterization of separating sets
of monomials is given in terms of zero-sum sequences over abelian groups.
