Towards the end of this article (https://io9.gizmodo.com/what-would-the-earth-be-like-if-it-was-the-shape-of-a-d-1515700296) there is mention of the different kinds of orbits the moon of a Torus world could have.
Many of the more wild and crazy orbits would result in the moon becoming unstable and crashing into the planet. However, I'm interested in another possibility.
Could a Torus world have a system of planetary Rings?
Edit: To elaborate, would any of the more unconventional orbits mentioned in the article (particularity ones that process into a rosette) form a distinct set of rings, or would it end up as an indistinct cloud of dust?