Question related to gravity in a hollow sphere

Ok, so I might have something totally wrong here but anyway, just out of curiosity.

Considering a uniform hollow sphere, the gravitational pull outside of it pulls towards its centre but at any location inside it there is no net pull towards any point.
In 2 dimensions, does a ring have the same properties? And if there's a ring in 3 dimensions, does it have the same properties on the plane of the ring, what happens to gravity when moving perpendicular to the plane?

Thanks for any thoughts on this.