Let $(R,m)$ be a one-dimensional Noetherian domain. Is $R$ a regular or a topical ring like Gorenstein or other kinds?
2026-03-25 15:54:36.1774454076
One dimensional noetherian domain
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It is a Cohen Macaulay ring; since every none-zero element is a none-zerodivisor and therefore $depth\ R =1$.
If in addition $R$ be a PID then it will be regular, and so Complete intersection and Gorenstein