Injective resection of the ring of complete functions.

Leave $ R $ Be the ring of full functions. I heard that the concrete value of the overall dimension of the ring depends on the continuum hypothesis.
I would think that the injective dimension of the regular module $ R $ It should match the overall dimension of this ring, but I'm not sure.

Question: Can you write an explicit (minimum) injective resolution of the regular module? $ R $? How do you see it if possible?