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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 1st 2024
   • (edited Mar 1st 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAn edit to *[[normed ring]]* is being discussed in another thread, [here](https://nforum.ncatlab.org/discussion/17818/normed-ring/?Focus=116027#Comment_116027). <a href="https://ncatlab.org/nlab/revision/diff/normed+ring/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/normed+ring/11">v11</a>, <a href="https://ncatlab.org/nlab/show/normed+ring">current</a>

   An edit to normed ring is being discussed in another thread, here.

   diff, v11, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 2nd 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the original reference: * [[Israel Gelfand]], *Normierte Ringe*, Rec. Math. [Mat. Sbornik] N.S. **9**(51) 1 (1941) 3–24 &lbrack;[mathnet:6046](https://m.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=6046&option_lang=eng)&rbrack; For what it's worth, the extra axiom in not stated there, either. <a href="https://ncatlab.org/nlab/revision/diff/normed+ring/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/normed+ring/14">v14</a>, <a href="https://ncatlab.org/nlab/show/normed+ring">current</a>

   added the original reference:

   • Israel Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N.S. 9(51) 1 (1941) 3–24 [mathnet:6046]

   For what it’s worth, the extra axiom in not stated there, either.

   diff, v14, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 2nd 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn [Bosch, Güntzer & Remmert 1984](https://ncatlab.org/nlab/show/normed+ring#BoschGüntzerRemmert84) the axiom is also not stated, but they prove that it follows from their axioms (Prop. 3). <a href="https://ncatlab.org/nlab/revision/diff/normed+ring/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/normed+ring/14">v14</a>, <a href="https://ncatlab.org/nlab/show/normed+ring">current</a>

   In Bosch, Güntzer & Remmert 1984 the axiom is also not stated, but they prove that it follows from their axioms (Prop. 3).

   diff, v14, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 3rd 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * Shigeo Ozaki, Sadao Kashiwagi, Teruo Tsuboi, *Note on Normed Rings*, Science Reports of the Tokyo Bunrika Daigaku, Section A **4** 98/103 (1953) 277-282 &lbrack;[jstor:43700402](https://www.jstor.org/stable/43700402)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/normed+ring/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/normed+ring/16">v16</a>, <a href="https://ncatlab.org/nlab/show/normed+ring">current</a>

   added pointer to:

   • Shigeo Ozaki, Sadao Kashiwagi, Teruo Tsuboi, Note on Normed Rings, Science Reports of the Tokyo Bunrika Daigaku, Section A 4 98/103 (1953) 277-282 [jstor:43700402]

   diff, v16, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 3rd 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexAfter the definition ([here](https://ncatlab.org/nlab/show/normed+ring#NormedCommutativeRing)), I have replaced the pointer to [Berkovich 2009, def. 1.2.1](https://ncatlab.org/nlab/show/normed+ring#Berkovich09) and the claim that Berkovich is missing an axiom (instead the issue seems to be that Berkovich discusses the non-Archimedean case) by pointer to [Ozaki, Kashiwagi & Tsuboi 1953](https://ncatlab.org/nlab/show/normed+ring#OzakiKashiwagiTsuboi53). <a href="https://ncatlab.org/nlab/revision/diff/normed+ring/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/normed+ring/17">v17</a>, <a href="https://ncatlab.org/nlab/show/normed+ring">current</a>

   After the definition (here), I have replaced the pointer to Berkovich 2009, def. 1.2.1 and the claim that Berkovich is missing an axiom (instead the issue seems to be that Berkovich discusses the non-Archimedean case) by pointer to Ozaki, Kashiwagi & Tsuboi 1953.

   diff, v17, current