  I derive separability inequalities for Bell correlations of observables in
arbitrary pure or mixed $N$ Qudit states in $D^N$-dimensional state space. I
find states (a continuum of states if $D>3$) including maximally entangled
states which violate these inequalities by a factor $2^{N-1}$ ; local reality
Bell inequalities are much weaker, their maximum violation being by a factor
$2^{(N-1)/2}$. The separability inequalities allow tests of entanglement of
unknown states using only the measured correlations .
