wrote:

ring is a set with two specified operations called multiplication and addition. ring is an algebrain group by addition and a monoid by multiplication

Algebraic, you mean.

WTF does this have to do with a piece of jewelry?

do you wanna look at my ring?
sorry couldnt resist it ...

Alex : Why do u want to write anythign on that ring ?
That would only curtail its use.

If u put your name : Well it starts to looks like an engagement ring.
If you put someone else's name : Err, it still looks like an engagement ring

If you put something stupid like what some of the people here suggested.. it might look "Cool" now, but lets say 5 years from now.. err. do u still want to wear it ?

If its pure gold, then my suggesstion, present it to your Mom / Sister or GF. They will apprecite it more than you. ( Assumuing you are a man here )
and dont engrave anything on it .

Congrats on getting that gift.

get it engraved with NO 1 excessiveplus player and have a competition and charge a small fee to enter and give it as a prize..