invisibility

This may be a totally dumb question, but it had me wondering... How come the chain that Frodo has around his neck doesn't turn invisible when he puts it through the one ring? ~V~

The Nazgul are Wringwraiths, invisible in the real world. But they were once men before the Nine Rings ensnared them and eventually turned them into invisible wraiths. Did the Nine Rings always make them invisibile when they wore the Rings or was invisibility at first under their control...

We know that the One Ring rendered the wearer of it invisible. But did the Ring actually go invisible itself? Or did it look like a Ring that floated around in mid-air like when the Lord of the Nazgul reveals himself and all you can see is a crown? Any opinions?

Was Sauron invisible when he wore the ring? If not, why not? If so, how was the ring cut from his hand?

The Ring - not being seen - Tom B THE ring of Power makes you invisible. I've had an arguement that old Tom B was NOT a Maia because when he put the ring on he remained visible and was therefore immune to its power, (Whilst Gandalf etc felt the power of the Ring) unlike everyone else. Me...