A finite direct product of Cohen-Macaulay rings is a Cohen-Macaulay ring. It could be checked by a scrutiny into localization of a finite direct product of rings at a prime ideal of the product. Now, does the statement remain true if "finite" is replaced by "infinite"? Any leading answer is appreciated.
2026-03-25 16:13:39.1774455219
Infinite direct product of C-M rings
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This question is not well-posed: an infinite direct product of fields is not even a noetherian ring.