Is a binary system of two planets with a common ring possible?

I want to have two planets orbiting each other, and there is a ring around both of them, is this possible?

I know rings are formed inside the Roche limit, so if the ring lies outside the planets, the material of the planets should be far harder than that of the ring, is it correct?

And a more important problem: can a binary system hold a common ring if a suitable substance is available?

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Is a binary system of two planets with a common ring possible?

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