The Ring of Invisibility is an interesting item with a strange name—but that's not what this document is about. This document is about the standard Rings that three wise women will bestow upon you during your journey.
These Rings are not vital to the completion of your quest. There are three wise women who will not speak to you unless you bring them a Ring, and only one of the three hints they give is useful at all. (Admittedly, it's extremely useful, but you have a guide for that sort of thing.) Any of the three Rings will allow you to speak to any of the wise women, but they will take the Ring after you do so. The wise woman who took the Ring will continue giving hints if you visit her again, but you'll need to find other Rings to speak to the other two.
There is an interesting bug/oversight with regards to the Rings: if you defeat Golvellius with any in your inventory, and then continue, you will start a new game, but you'll still have the Rings. Useful? No. But potentially interesting! (OK, probably not.)