Saruman taking ring from Gandalf..

[Rosenberg]

Getting back to the original question--knowing Saruman knew Gandalf had that ring, there would have to be a very good reason he didn't take it. Maybe he did hide it from Saruman, decieving him into thinking he left it somewhere for safe keeping perhaps. Or maybe becaues the ring was Elven, it would have somehow conflicted with the One Ring of Sauron or its power in some way. Whatever it is, Tolkien doesn't explain it, and none of the characters seem to think it odd that Saruman didn't take a potential weapon from his enemy.