Talk:Regular ring: Difference between revisions

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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)[reply]

The two definitions are not equivalent

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)[reply]

Fixed this. Added few more references. Kammerer55 (talk) 04:26, 2 May 2017 (UTC)[reply]

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 == 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:Zdorovo|Zdorovo]] ([[User talk:Zdorovo|talk]]) 21:21, 3 December 2015 (UTC)
+:Fixed this. Added few more references. [[User:Kammerer55|Kammerer55]] ([[User talk:Kammerer55|talk]]) 04:26, 2 May 2017 (UTC)