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I wonder what the correct noun for the adjective "Noetherian" is. Should I say

"By Noetherianess of $R$, the ideal $I\subseteq R$ can be generated by finitely many elements." or

"By Noetherianity of $R$, the ideal $I\subseteq R$ can be generated by finitely many elements."?

Thanks for your answers!

Luvath
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    "-ness" seems to be proper suffix. On the other hand, "-ity" may also be valid. – user170231 Aug 17 '22 at 20:08
  • In similarly to "evenness," it should be "Noetherianness" with two n's. – Thomas Andrews Aug 17 '22 at 20:09
  • English is not really a language of strict rules, specially when building nouns and verbs. My personal taste likes "Noetherianity" better. – plop Aug 17 '22 at 20:09
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    Noetherianess would be an archaic term for a woman Noetherian ring. :) – Thomas Andrews Aug 17 '22 at 20:10
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    "Because the ring $R$ is Noetherian, ...." – Andrew D. Hwang Aug 17 '22 at 20:11
  • I had to write something like this in a formal paper this week, and my cop-out solution was to write the equivalent of, "By the Noetherian condition on $R\dots$" – anomaly Aug 17 '22 at 20:16
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    But, to get back to the "evenness" example, I barely even see evenness used by real mathematicians. And I think saying "By the Noetherian property, .the ideal .." without specifying $R$ here. Noetherianness and Noetherianity are both terrible. – Thomas Andrews Aug 17 '22 at 20:35
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    For example, M.SE has only 349 pages that use evenness as a word. Compared to >200K that use the word "even." And some of those use "evenness" for an informal measure of the degree that a distribution is uniform, rather than any binary notion of even/odd. – Thomas Andrews Aug 17 '22 at 20:39

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