Talk:Hilbert's basis theorem

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Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. So called 'proof' needs to go. On the other hand, the various implications, including the history, have to be thoroughly explained. Arcfrk 04:22, 28 June 2007 (UTC)

Surely the Hilbert Basis Theorem fails when there is an infinite number of variables. If this is the case, then the theorem needs to be specified a little more precisely.

Best Wishes, Max Murphy (Dr, Permutation Patterns).

[edit] slightly more general?

immediately following is the case of a single variable, without multidegrees etc., it doesn't read well. 24.59.111.68 05:44, 15 November 2007 (UTC)

• the proposition "R Noetherian --> R[X] Noetherian" is a chainable proposition : If R is Noetherian then R[X] is Noetherian and so (R[X])[Y] is Noetherian and (R[X])[Y] is just R[X,Y] and so on. —Preceding unsigned comment added by Novwik (talk • contribs) 21:22, 29 December 2007 (UTC)