  For any quantum state representing a physical system of identical particles,
the density operator must satisfy the symmetrisation principle (SP) and for
massive particles also conform to super-selection rules (SSR) that prohibit
coherences between differing total particle numbers. Here we consider
bi-partitite states for systems of massive bosons, where both the system and
subsystems are modes (or sets of modes), particles being associated with
differing mode occupancies. To define non-entangled or separable states the
subsystem density operators are also required to satisfy the SP and conform to
SSR, in contrast to some other approaches. Whilst in the presence of these
additional constraints some of the known entanglement criteria are still valid,
we present a detailed treatment to establish the validity of known criteria and
derive new ones.
