The Dwarven rings could turn you invisible. All the rings could (except possibly the elven ones). The reason the dwarves do not turn invisible is because of their great willpower. That is also why Sauron could not corrupt them like he did with men. All he could do was make the holders of the rings more greedy. It says all this in one of the appendixes or unfinished tails (I'm not sure which). Kind of similar to when Tom Bombadil does not turn invisible. The rings could not dominate dwarves the way they dominate men.
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