Real part of the dimensionless wave frequency Re(ω) versus the dimensionless Alfvén frequency a = kV_A/ω_i in partially ionized plasmas, where ω_i is the ion gyro-frequency. a) Single-fluid MHD equations with inertial term (dispersion relation given by Eq. (30)); b) single-fluid Hall MHD equations (dispersion relation given by Eq. (31)); c) single-fluid MHD equations without modified Hall current (dispersion relation given by Eq. (35)); d) zoom of the solutions in panels b) (green line) and c) (red line) near x axis.