Are those really the rings of the dead? That ring seems way too plain.
Gamma's reason for wanting them is to become immortal, but I'm sure there's much more to his story.
He takes Elwood to a CD store, which is actually a front for Gamma to get information privately. He's supposed to meet someone who claims to have found a ring. While this is happening, Elwood is waiting for Gamma, but he gets caught up with some guys who try to kill him for revenge against Gamma. Gamma shows up and easily takes care of them. He's got a cool fighting style.