The Shell Theory tells us that inside a homogeneous sphere there is no gravity. It seems to me that if you cut off the top and bottom of the sphere and leave a ring, equal in width from the equator of the sphere, that it, too, would have zero gravity within the ring along the plane of the original equator.
Please ignore the instability of the ring when rotating around a central mass such as a star or planet. Assume the ring has no substantial masses near it.
For the purpose of this question, the ring is not spinning, so there is no centripetal force.
Question: In this instance, would a person standing on the inside of the ring, or at any point within the volume of space defined by the circumference and width of the ring, experience a gravitational effect due to the ring?