  We develop a general theory of buoyancy instabilities in the electron-ion
plasma with the electron heat flux based not upon MHD equations, but using a
multicomponent plasma approach in which the momentum equation is solved for
each species. We investigate the geometry in which the background magnetic
field is perpendicular to the gravity and stratification. General expressions
for the perturbed velocities are given without any simplifications. Collisions
between electrons and ions are taken into account in the momentum equations in
a general form, permitting us to consider both weakly and strongly collisional
objects. However, the electron heat flux is assumed to be directed along the
magnetic field that implies a weakly collisional case. Using simplifications
justified for an investigation of buoyancy instabilities with the electron
thermal flux, we derive simple dispersion relations both for collisionless and
collisional cases for arbitrary directions of the wave vector. The
collisionless dispersion relation considerably differs from that obtained in
the MHD framework and is similar to the Schwarzschild's criterion. This
difference is connected with simplified assumptions used in the MHD analysis of
buoyancy instabilities and with the role of the longitudinal electric field
perturbation which is not captured by the ideal MHD equations. The results
obtained can be applied to clusters of galaxies and other astrophysical
objects.
