  In this paper we show that Z_8 does not admit a natural duality. In fact, we
show that 2Z_8 = {2, 4, 6, 8 | +,.} is not dualizable, and this will imply that
the original ring is not dualizable, either. As a corollary we show that
Sindi's conjecture does not hold. Our technique will be similar to one due to
Quackenbush and Szab\'o, where non-dualizability is proved for the quaternion
group.
