The transporter wouldn't be able to disassemble the one ring. In universe, my assumption is that they wouldn't even be able to get a sensor lock on it.
Probably couldn't transport anyone carrying the ring either.
And the capability to create as many copies of that ring as you want, actually.
Just one copy of "the one ring" would cause chaos. Now, imagine a hundred million of those fuckers on the open market! While some of the immediate side effects might be a bit weird, but it seems like the entire system of control might collapse fairly quick.
Leak a copy of the transport buffer to China, while we are at it, and we should be seeing those show up on EBay for $1.99 in about a week or so.
It would be interesting if the ring ever made its way onto DS9 and into Quark's hands. Everyone would wonder why he's obsessing about a ring made of worthless gold.