[Thinlómien]

I think we have a problem of definition here. You say, that any ring with magic abilities is a ring of power. (Right?) I use the name ring of power only for really significant items, such as the 19 rings made by the elf smiths and the One Ring.

My theory about Saruman's ring, however, is that it was a lesser ring with little magical power, or it was only a status symbol, or that it was a creation of Saruman, who had tried to create a powerful item (and probably failed by the way).