Detecting full N-particle entanglement in arbitrarily-high-dimensional systems with Bell-type inequalities

We derive a set of Bell-type inequalities for arbitrarily-high-dimensional systems based on the assumption of partial separability in the hybrid local-nonlocal hidden-variable model. Partially entangled states would not violate the inequalities, and thus, upon violation, these Bell-type inequalities are sufficient conditions to detect the full N-particle entanglement and invalidity of the hybrid local-nonlocal hidden-variable description.