Talk:Noetherian ring

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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. Needs a proper lead, and also references. Geometry guy 21:15, 31 May 2007 (UTC)

[edit] Ideals of Q

The article states that noetherian implies every ideal is finitely generated; shouldn't that be every proper ideal is finitely generated, since for example, Q is noetherian (every field is), and yet Q cannot be finitely generated? Chas zzz brown 20:11 Apr 2, 2003 (UTC)

Never mind. Q is finitely generated - as an ideal. Chas zzz brown 10:22 Apr 3, 2003 (UTC)

[edit] Large

The article says: "Rings that are not Noetherian tend to be (in some sense) very large." I dont know what this should mean, since there are many examples of non-noetherian subrings of (not very large) noetherian rings. For example, there are non-noetherian subrings of k[X,Y]. ( k[X,Y] the ring of polynomials in two variables over a field k) 84.154.252.105 14:43, 8 April 2007 (UTC)

I added two examples to ensure that the "large" comment is not taken too formally. I suspect all k-subalgebras of k[x,y] itself are noetherian, but I gave the reasonably standard example of a non-noetherian subring of k(x,y) that is a non-finitely generated module over k[x,y]. JackSchmidt (talk) 15:13, 22 May 2009 (UTC)

[edit] lower case 'n'?

This should be discussed in the article, but shouldn't "n" in "Noetherian" be lower-cased, just like abelian. -- Taku (talk) 23:02, 19 December 2008 (UTC)

Use of lower case for adjectives named after mathematicians is commonplace in French, but is all but unheard of in English. The word abelian is a notable exception to this rule. (I have never heard a convincing explanation for why this one word is not capitalized, but it invariably isn't.) Plclark (talk) 06:58, 24 December 2008 (UTC)

It is not uncommon for noetherian and artinian to be lower case in mathematical English, but less common than for abelian. I don't think it's worth changing one way or the other. Another silly example is whether the φ in Frattini subgroup should be capitalized; it usually is, but not always. Mathematical English is a very international language, and it shouldn't be surprising that its rules are complex and somewhat incomprehensible. JackSchmidt (talk) 18:08, 24 December 2008 (UTC)

The common convention is to use lower case on "noetherian", as she was a woman. —Preceding unsigned comment added by 138.246.7.139 (talk) 09:47, 22 May 2009 (UTC)