  The anticommuting properties of fermionic operators, together with the
presence of parity conservation, affect the concept of entanglement in a
composite fermionic system. Hence different points of view can give rise to
different reasonable definitions of separable and entangled states. Here we
analyze these possibilities and the relationship between the different classes
of separable states. We illustrate the differences by providing a complete
characterization of all the sets defined for systems of two fermionic modes.
The results are applied to Gibbs states of infinite chains of fermions whose
interaction corresponds to a XY-Hamiltonian with transverse magnetic field.
