A ring. A circle. Begin wherever, End never. No sharp edges, no points. Just an infinite circle, an endless cycle. It can mean a promise, a reminder, a symbol. But, It is no longer a ring if broken. No glue can return it to its original shape Before the break.
Conspiracy theory: Lord of the Rings is about marriage and is full of symbolic meaning. Gollum is desperate for marriage. Ever since he became ugly, he knew that it would mean that nobody would want him. But maybe if he has a ring, he will feel some of the feelings of the bond of marriage and the feeling of love.