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Sep 7, 2022 at 13:49 comment added pop1 Thank you for your answer. I remember that $R^+$ could not be Cohen-Macaulay in the case that $R$ has equal-characteristic 0, so the answer is negtive for such $R$.
Sep 7, 2022 at 12:55 history answered Laurent Moret-Bailly CC BY-SA 4.0