You shouldn't have any problems in the carry on or in your pockets, people stroll through the detectors all day without taking off their rings. Bringing it into another country should be no problem at all, I don't think we have ever been uestioned entering any country but when coming back to the states.

You should bring a receipt with you though, when you come back they may want to charge you duty if you can't prove you purchased it in the states.

Women who just got a diamond have a nasty habit of answering every question wtih "Take a look at my brand new ring" so when Customs asks if you have anything to declare.... it's better to have the receipt.