Talk:Noetherian ring

message: 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)
replies: text: 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)
thread_title:  Large 

message: 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)
replies: text: 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)

text: 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)
replies: text: 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)
replies: text: That is, for obvious reasons, an unconvincing argument. PST 11:06, 23 May 2010 (UTC)
thread_title:  lower case 'n'? 

message: There really should be something about Dedekind rings in this article since the "typical proof" that non-zero ideals in Dedekind rings can be uniquely factorized into a product of powers of prime ideals (roughly speaking) relies on a couple of basic facts of Noetherian rings. Also, Dedekind rings are ubiquituous in number theory and commutative algebra. I suspect Plclark is an expert on these matters as he seems to have contributed to the article Dedekind domain, but if no-one adds something about Dedekind domains here, I can always do so. PST 01:47, 7 August 2010 (UTC)
thread_title:  Dedekind domains 

message: "...if a ring is Noetherian, then it satisfies the descending chain condition on prime ideals." Is this really true?  — Preceding unsigned comment added by UqSL2 (talk • contribs) 22:02, 25 January 2012 (UTC)
thread_title:  DCC on prime ideals 

message: A while back User:TakuyaMurata removed a long expository section which User:Point-set topologist recently reinstated. I reverted to restore Taku's version because I think his earlier removal was probably the right way to go. As it was, it was a bit long and apparently springs out of personal thoughts, and wasn't citable and wasn't really encyclopedic. It also served as a fairly big text barrier against the main information in the article in the next section. I'm sure some of the information thta used to be there can find a home elsewhere in the article, though. Rschwieb (talk) 18:17, 31 July 2013 (UTC)
replies: text: A shorter version successfully describing the basic nature of Noetherian rings would be good. But it should be conveyed without descending into a homegrown exposition about them. I'm in agreement with Taku's description of a "good introduction" in the last paragraph. Rschwieb (talk) 12:51, 2 August 2013 (UTC)
thread_title:  Long "introduction" section 

message: This is probably elementary but what is a ring that is not a subring of a Noetherian ring? -- Taku (talk) 00:12, 25 August 2015 (UTC)
thread_title:  A ring that is not a subring of a Noetherian ring 

message: It's unclear whether any or all of the results on this page require the ring to be unital. The article on "Ring (mathematics)" specifies that within that article, "ring" means "unital ring", but I'm not sure whether the authors of this article used the same convention. Can someone with more expertise judge whether this article should state somewhere that it assumes all rings are unital?  — Preceding unsigned comment added by 2604:3D08:297F:7000:45D1:141:808C:BAAD (talk) 19:37, 5 December 2020 (UTC)
replies: text: Ring is linked in the first sentence. This means that it is the definition of this article that is assumed. So the answer to your question is yes, in this article rings are unital. Otherwise, this would be the term of rig that would have been used. D.Lazard (talk) 20:41, 5 December 2020 (UTC)
replies: text:  Did you mean rig or rng? 2A00:23C7:7B18:9600:5575:4A4C:2A45:AD28 (talk) 10:22, 22 June 2021 (UTC)
replies: text:  Yes, rng. D.Lazard (talk) 11:35, 22 June 2021 (UTC)
thread_title:  Unitality 

message: Any clues as to standard English pronunciation?  Something like \nʌθiɹi.ən\ or  \nøːtɐɹi.ən\ or \noʊiːθəɹi.ən\ ? 2A00:23C7:7B18:9600:5575:4A4C:2A45:AD28 (talk) 10:17, 22 June 2021 (UTC)
thread_title:  Pronunciation