LotR -- Book 6 - Chapter 2 - The Land of Shadow

[Kuruharan]

Now I'm afraid I'm going to have to turn the tables and ask you to explain how that is possible.

-and-

If you ask me, the "soul" behind the Ring is not a fea but an eala - specifically, Sauron.

Hmm...you may have a point about that. Hasty choice of words on my part.

However, I don't think that the part of Sauron that went into the Ring was entirely "Sauron" after that point. I think it was something else...note how if somebody else (read Gandalf) claimed the Ring and mastered it the Ring would be able to survive even though Sauron's spirit would be permanently broken.