What are the rings on the bottom of a frying pan called and can you use them on a glass cooktop?
The concentric rings can serve a variety of purposes. In addition to helping to prevent the pan from sliding, they increase the surface area of the bottom of the pan, which helps it to get heat more efficiently from a gas range.

On some pans, these concentric rings are made of different metals (aluminum or copper) and act to more effectively spread heat around the pan.

I have used pans with textured bottoms on ceramic ranges before with no problems. As always, you will want to avoid repeated shaking motions (say, popcorn) but it's otherwise not a big deal either way.