How do you get the rings off an older glass cooktop?

I use this product on a lot of things. It's great at getting scratches out of CDs and DVDs. I'll bet it would get those rings off of your cooktop. You can pick up a bottle at any auto parts store.

[image deleted]

Backing soda and water. It's gritty enough to get stuff off. If it worse than that use a razor blade and shave it off.

There's a product called Ambersil - it's a trade product and few people know of it.