Talk:Regular ring: Difference between revisions
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{{merged-to|Regular local ring#Regular ring|14 September 2020}} |
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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) |
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Latest revision as of 11:59, 29 January 2024
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 | 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)