UFD imply ACCP (ascending chain condition for principal ideals). But is it necessarily UFD implies ACC also (ascending chain condition for ideals)?
2026-03-29 12:42:16.1774788136
Does UFD imply ACC?
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No. If $K$ is a field, $K[X_1,X_2,\dots, X_n,\dots]$ is an example of a non-noetherian UFD.