We　study　separability　criteria　in　multipartite　quantum　systems　of　arbitrary　dimensions　by　using　the　Bloch　representation　of　density　matrices.　We　first　derive　the　norms　of　the　correlation　tensors　and　obtain　the　necessary　conditions　for　separability　under　partition　of　tripartite　and　four-partite　quantum　states.　Moreover,　based　on　the　norms　of　the　correlation　tensors,　we　obtain　the　separability　criteria　by　matrix　method.　Using　detailed　examples,　our　results　are　seen　to　be　able　to　detect　more　entangled　states　than　previous　studies.　Finally,　necessary　conditions　of　separability　for　multipartite　systems　are　given　under　arbitrary　partition.