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Qing Liu
Qing Liu
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If I understand correctly (1), the property of being a PID (including fields) isfollowing properties are not local. Neither being Noetherian.

  • being a PID (including fields): take a non principal Dedekind domain;
  • being Noetherian (consider an infinite product of $\mathbb F_2$);
  • being Artinian (same example as above).

If I understand correctly (1), the property of being a PID (including fields) is not local. Neither being Noetherian.

If I understand correctly (1), the following properties are not local

  • being a PID (including fields): take a non principal Dedekind domain;
  • being Noetherian (consider an infinite product of $\mathbb F_2$);
  • being Artinian (same example as above).
Source Link
Qing Liu
Qing Liu
  • 11.1k
  • 1
  • 42
  • 50

If I understand correctly (1), the property of being a PID (including fields) is not local. Neither being Noetherian.