Talk:Regular ring: Difference between revisions
Content deleted Content added
Kammerer55 (talk | contribs) No edit summary |
Tag: |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{WikiProject banner shell| |
|||
{{maths rating |
|||
{{WikiProject Mathematics}} |
|||
|field=algebra |
|||
|importance=low |
|||
|class=stub |
|||
|vital= |
|||
|historical= |
|||
}} |
}} |
||
{{merged-to|Regular local ring#Regular ring|14 September 2020}} |
|||
This is not a disambiguation page, since the (first) notion of "regular ring" does not have its own page!--[[User:129.70.14.128|129.70.14.128]] 21:03, 24 October 2007 (UTC) |
This is not a disambiguation page, since the (first) notion of "regular ring" does not have its own page!--[[User:129.70.14.128|129.70.14.128]] 21:03, 24 October 2007 (UTC) |
||
| Line 11: | Line 8: | ||
== The two definitions are not equivalent == |
== The two definitions are not equivalent == |
||
Serre's definition of a regular ring is not equivalent to the other one. For instance, [http://mathoverflow.net/questions/21067/noetherian-rings-of-infinite-krull-dimension Nagata's example] of a Noetherian ring with infinite Krull dimension satisfies the first definition of a regular ring, but fails Serre's defintion. The two definitions are only equivalent for rings of finite dimension. Accordingly, the statement that Serre proved the definitions are equivalent needs a source. |
Serre's definition of a regular ring is not equivalent to the other one. For instance, [http://mathoverflow.net/questions/21067/noetherian-rings-of-infinite-krull-dimension Nagata's example] of a Noetherian ring with infinite Krull dimension satisfies the first definition of a regular ring, but fails Serre's defintion. The two definitions are only equivalent for rings of finite dimension. Accordingly, the statement that Serre proved the definitions are equivalent needs a source. [[User:Zdorovo|Zdorovo]] ([[User talk:Zdorovo|talk]]) 21:21, 3 December 2015 (UTC) |
||
[[User: |
:Fixed this. Added few more references. [[User:Kammerer55|Kammerer55]] ([[User talk:Kammerer55|talk]]) 04:26, 2 May 2017 (UTC) |
||
Latest revision as of 11:59, 29 January 2024
 | This redirect does not require a rating on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | |||||||
| ||||||||
 | The contents of the Regular ring page were merged into Regular local ring#Regular ring on 14 September 2020. For the contribution history and old versions of the merged article please see its history. |
This is not a disambiguation page, since the (first) notion of "regular ring" does not have its own page!--129.70.14.128 21:03, 24 October 2007 (UTC)
The two definitions are not equivalent
[edit]Serre's definition of a regular ring is not equivalent to the other one. For instance, Nagata's example of a Noetherian ring with infinite Krull dimension satisfies the first definition of a regular ring, but fails Serre's defintion. The two definitions are only equivalent for rings of finite dimension. Accordingly, the statement that Serre proved the definitions are equivalent needs a source. Zdorovo (talk) 21:21, 3 December 2015 (UTC)
- Fixed this. Added few more references. Kammerer55 (talk) 04:26, 2 May 2017 (UTC)