  In the paper we comment on (R\"udiger & Shalybkov, Phys. Rev. E. 69, 016303
(2004) (RS)), the instability of the Taylor--Couette flow interacting with a
homogeneous background field subject to Hall effect is studied. We correct a
falsely generalizing interpretation of results presented there which could be
taken to disprove the existence of the Hall--drift induced magnetic instability
described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103. It is shown
that in contrast to what is suggested by RS, no additional shear flow is
necessary to enable such an instability with a non--potential magnetic
background field, whereas for a curl--free one it is. In the latter case, the
instabilities found in RS in situations where neither a hydrodynamic nor a
magneto--rotational instability exists are demonstrated to be most likely
magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are
clarified.
