There is a Singapore law that states if you find a valuable item, such as a ring, you must make an attempt to find the owner if possible. It is the responsibility of the finder to show an attemopt to locate the owner.
That said, if here are no markings that would make the jewelry identifiable, then this may not be possible. It's not an easy law to enforce, or to obey. However, if you find a ring next to a person on the beach, and they see it, they may claim they just lost it and the law will be on their side (I have never experienced this). I would keep all found jewelry hidden until after you leave the beach. That way, you can inspect it in private, and if there is a name or other identifying mark you can choose if you wish to make the effort to locate the owner.
Bottom line - if you are caught with found jewelry and have made no effort to find the owner you are then technicaly guilty of the crime of "Misappropriation of Personal Property": with a possible jail term of 2 years. This is not a law that is too difficult to enforce, and the Singapore police I work with have never seen it brought up. They suspect that they would need to have a case where the owner of the said jewelry could show that not only the jewelry was theirs, but also that you KNEW it was theirs and kept it anyway. Only then I believe the police would bring a case against you, as there is no such thing as "Finders Keepers, Loosers weepers". If an object can be traced to an individual, they have the right to get it back, even if they left it on the beach a year ago!