By alchemist do you mean alchemy by Ben Seidman? If yes then yes, you can turn a coin into a ring quite easily, to go the other way though, or to just vanish the ring, I'd say no, if it was maybe the flattest ring you can get then maybe, probably not.
To change into a ring, yes, to vanish a ring, don't buy it, unless you plan to use it for its intended purpose.