Was Saruman's ring subject to the one ring as well?

Saruman was known to of studied ring-lore and the rings created by the elves and Sauron, he probably created his own ring in the fashion the elves of Eregion did who had help from Sauron. We know that even though Sauron played no part in creating the 3 elven rings made personally by Celebrimbor were still subject to the one ring mainly because of how great the one ring was and maybe because they were made in the same fashion as the other rings and the one.

We also know after isengard was defeated and his staff was broken by Gandalf, Saruman still had some decent power left aka his voice and even uses his voice to make treebeard release him from isengard, yet once the one ring was destroyed Saruman seemed to have no power left whatsoever. Which makes it seem that his ring enhanced him even when his staff was broken, but like the other rings once the one ring was destroyed his ring failed.

Is there any evidence that may back this up?