  We investigate the genuine entanglement in tripartite systems based on
partial transposition and the norm of correlation tensors of the density
matrices. We first derive an analytical sufficient criterion to detect genuine
entanglement of tripartite qubit quantum states combining with the partial
transposition of the density matrices. Then we use the norm of correlation
tensors to study genuine entanglement for tripartite qudit quantum states and
obtain a genuine entanglement criterion by constructing certain matrices. With
detailed examples our results are seen to be able to detect more genuine
tripartite entangled states than previous studies.
