Talk:Poincaré–Birkhoff–Witt theorem

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Isn't the proof idea at the end misleading without additional comment?

  • The point there is a unique reduction is missing;
  • The fact that there is a reduction at all is not at all clear by applying the structure equations. One needs something like induction on the degree of the canonical monomial; thus
A u v B = A v u B + \sum_z c_{u v z} A z B \quad

where the suummands

\sum_z c_{u v z} A z B \quad

have lower degree and thus are reducible by the induction hypothesis.

Including this on the other hand seems overkill.CSTAR 23:14, 6 Sep 2004 (UTC)

[edit] History

I am told that neither Henri Poincaré nor Birkhoff nor Witt gave a correct proof. I say the article should say a few words about the history of the theorem and who eventually proved it. At the very least the article should have links to the mathematicians above! Mhym 04:54, 22 March 2006 (UTC)

It would be nice mention in the article who the theorem is named for, with links to their own articles.--BillFlis 16:55, 31 March 2006 (UTC)
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