Talk:Noether Normalization Lemma

A few quick comments on this:


 * a) A definition needs to be put in place for "k-algebra". The Wikipedia page is unclear (such lack of clarity was one of the reasons why ProofWiki was put together in the first place). Several other terms need to be linked to, some of which already exist on ProofWiki but others I believe may not.


 * b) Suggest this page might be renamed Noether Normalization Lemma as this is what it seems to be called in general. The title "Noether Normalization" sounds as though it might be a "definition" as opposed to a "theorem" because it sounds like it's a process, a thing you do to normalize whatever it is that is being normalized. Exactly what is being normalized is not clear.


 * c) The Wikipedia article on this subject suggests that $$A$$ needs to be a commutative k-Algebra which is also an integral domain. Is this necessary, or is the result posted here more general than Wikipedia?

--prime mover 09:37, 2 January 2011 (UTC)

A few quick answers
 * a) I will try to make the wanted definitions. For clarity: a $$k$$-algebra is a commutative unital algebra over the field $$k$$.


 * b) I've seen it as Noether normalization, but the book from Atiyah and Macdonald calls it also as Noether's normalization lemma. (Ex. 16, chapter 5)

So it is up to you if you want to change it.


 * c) $$A$$ should as pointed out in a) be commutative, but may possess zero-divisors.

--Elfangor  15:06, 2 January 2011