[Raynor]

Originally Posted by Mänwë

It was I agree the Ring his life revolved around after his fall.

I disagree; after his fall, he believed the ring was lost:

Originally Posted by The Shadow of the Past, FotR

And this is the dreadful chance, Frodo. He believed that the One had perished; that the Elves had destroyed it, as should have been done. But he knows now that it has _not_ perished, that it has been found. So he is seeking it, seeking it, and all his thought is bent on it. It is his great hope and our great fear.

So Sauron believed the ring perished; after that, he merrily returned to conquering the world again, in the name of evil. Even after he learns about the existence of the ring, he peacefully continues his plans of beating the living bejesus out of Middle Earth - we don't see Sauron deflecting the bulk of his efforts towards recovering the ring or, even less, overwhelming the Shire by force, due to some fixation he has with the ring; he doesn't drop his plans, he steadily builds up his forces. He chooses stealth in his attempts to recover; the nazgul go in hiding, he conceals their actions with sideways attacks. Even when he launches his untimely offensive, it is more or less in tone with his plans of conquest. My point is that Sauron shows he is capable of pursuing his own plans, independent of the ring; others, such as the ringbearers, or even Galadriel, face an almost indomitable pressure to alter all their behaviour and life to the corruption of the ring.