I am searching for a $2$-dimensional Cohen-Macaulay (normal or not) domain.
Thanks in advance for any suggestion.
2026-03-25 09:31:53.1774431113
2-dimensional Cohen-Macaulay domain
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How about $R[x]$ where $R$ is a discrete valuation ring, or more generally a Dedekind domain?
For me, a Dedekind domain is a Noetherian normal domain of dimension $1$ and a DVR is a regular local ring of dimension $1$. So in either case the ring $R[x]$ is $2$-dimensional.