  The recent discovery of rings and massive satellites around minor bodies and
dwarf planets suggests that they may often coexist, as for example around
Haumea. A ring perturbed by an oblate central body and by an inclined satellite
may disperse on a short timescale. The conditions under which a ring may
survive are explored both analytically and numerically. The trajectories of
ring particles are integrated under the influence of the gravitational field of
a triaxial ellipsoid and (a) massive satellite(s), including the effects of
collisions. A ring initially formed in the equatorial plane of the central body
will be disrupted if the satellite has an inclination in the Kozai Lidov regime
(39.2 < i < 144.8). For lower inclinations, the ring may relax to the satellite
orbital plane thanks to an intense collisional damping. On the other hand, a
significant J2 term easily suppresses the perturbations of an inclined
satellite within a critical semimajor axis, even in the case of Kozai Lidov
cycles. However, if the ring is initially inclined with respect to the
equatorial plane, the same J2 perturbations are not a protective factor but
instead disrupt the ring on a short timescale. The ring found around Haumea is
stable despite the rise in the impact velocities that is due to the asymmetric
shape of the the body and the presence of a 3:1 resonance with the rotation of
the central body. A ring close to an oblate central body should be searched for
in the proximity of the equatorial plane, where the J2 perturbations protect it
against the perturbations of an external inclined satellites. In an inclined
configuration, the J2 term is itself disruptive.
