When viewing the movie, pay particular attention to the scenes where David (Tom Cruise) and Sophia (Penelope Cruz) are sketching each other. If my memory serves me correctly (I only watched the movie once), as the scenes move back and forth from focusing on David and Sophia, it appears that Sophia is wearing a ring, then she is not, then it appears again. It is on (and off) her left, "ring" finger.

The scenes as shot do not provide an explanation as to why the ring appears and then disappears.

As well, it may even be a different ring on her finger a few scenes later when she is laying on the sofa.