DMG p. 138:
Additionally, a creature can't attune to more than one copy of an item. For example, a creature can't attune to more than one ring of protection at a time.
The DMG even uses the Ring of Protection as the example for having no more than one copy of an item attuned.
Thanks for looking it up. We may have a couple of players that are cheating (not rings, but dual-wielding weapons) without realizing it.