Talk:Integrality
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| Mathematics rating: | Start Class | Mid Priority | Field: Algebra | |||
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I am the creator of this page and I am writing in response to the proposal by SatyrTN for speedy deletion. This is only a stub — it's meant to be expanded, and it was created literally hours ago. It's intended to have more than just the definition, eventually. I think anybody who knows some commutative algebra knows that this will be a useful topic to have done. Joeldl 09:59, 13 February 2007 (UTC)
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[edit] Title of article
I'd like input on this: Should the article be renamed to Integral extension? This does not directly include the idea of an integral element (without considering the ring generated by the base ring and that element), but "integral extension" is a more likely search phrase than "integrality". I suppose an alternative would be Integral element, or Integral dependence. Joeldl (talk) 05:29, 13 March 2008 (UTC)
[edit] merging "Integrally Closed" into this page
The "Integrally Closed" page has a request for discussion regarding merging the "Integrally Closed" page into this page.
I vote for keeping them as separate pages. They are both useful in their own way, and, they really are two different concepts, even though they are within the same subject.
I think "if it ain't broke don't fix it" applies here. Also the merge operation has the possibility of "breakage" since the two pages contain different (and valuable IMHO) information.
It might be easier to maintain them as two separate pages. For example, the comment regarding Integrally Closed Groups in the Integrally Closed Talk section fits more natually with the context of separate pages.
I think that if the two pages are kept like they are, they should cross-reference each other at the "See also" section at the bottom because they have different information.
Keeping the two pages separate helps with the "search" problem mentioned in the previous note.
DeaconJohnFairfax (talk) 23:05, 30 June 2008 (UTC)
- I vote for the merger. It looks like this page is already set up to easily incorporate everything on the integrally closed page regarding rings (in the normal schemes subsection for example). I think it would be unnatural, the way this article is heading, to not encompass all the information from the ring part of the integrally closed page. Then the only reason to keep the integrally closed page would be if it were extensive enough to merit a "See main article" link from the integrality page.
- As for the content on ordered groups, this looks like it could be easily included as another paragraph in the article on ordered groups.
- The integrally closed page could then become a disambiguation page. RobHar (talk) 23:32, 30 June 2008 (UTC)
Good Idea! DeaconJohnFairfax (talk) 16:44, 1 July 2008 (UTC)
[edit] Title of Article
Regarding the title of this, I think "Integral Extensions" would be a better title than "Integrality." I like the plural (s) in the title because the page discusses Integral Extensions in a number of different contexts.
When I first saw the link to "Integrality" on the "Integrally Closed" page, I almost didn't go to it because I thought it would be talking about whether or not a rational number is an integer. In other words, I thought it might be an extremely elementary article.
Either "Integral extension" or Integral extensions" communicates the idea that this is advanced math, not elementary school (or grammar school) stuff. DeaconJohnFairfax (talk) 23:07, 30 June 2008 (UTC)
- I think the idea is that this page discusses the notion of integrality to various degress of generality. Not everything discussed here is about integral extensions, some of it is about integral morphisms, or integrality of non-affine schemes. I think integrality is probably a more appropriate title. RobHar (talk) 23:42, 30 June 2008 (UTC)
How about "Integrality in rings"?
I just noticed last night that Neukrick's new book on Class Field theory calls his section on Integrality, "Integrality." I also noticed that many Wikipedia math articles add a qualifier to specify what kind of Integrality they are talking about. I.e., this page does not talk about round (or integral) numbers versus numbers with fractional parts - like is done in elementary school). DeaconJohnFairfax (talk) 16:43, 1 July 2008 (UTC)
[edit] Integral closure of a ring
The article defines the integral closure of a reduced ring. Could someone with access to the reference add a note why/if reduced is required? 78.52.196.230 (talk) 11:02, 30 October 2008 (UTC)
[edit] Completely integrally closed
What does it mean? -- Taku (talk) 01:26, 14 March 2009 (UTC)
