[Neithan]

Now the Elves made many rings; but secretly Sauron made One Ring to rule all the others, and their power was bound up with it, to be subject wholly to it and to last only so long as it too should last.--The Sil

When Sauron created the One Ring, its power became tied together with the rings it controlled, regardless of who created them.

Moot point, because no one else made any, I know, but an interesting thought nonetheless.

Actually I think Saruman made a ring of his own.

He wore a ring on his finger ... Saruman, the wise, Saruman Ring-maker ...--FotR

So the question is, was Saruman's ring under the power of the One? I don't think so, I think that Sauron bound all the rings to his when he created it rather than giving the Ring the power to bind all rings made by the methods that he taught the Elves.