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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 20th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadded section about Bézout domains in constructive mathematics, most of the text copied from [[principal ideal domain]] Anonymous <a href="https://ncatlab.org/nlab/revision/diff/B%C3%A9zout+domain/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/B%C3%A9zout+domain/3">v3</a>, <a href="https://ncatlab.org/nlab/show/B%C3%A9zout+domain">current</a>

   added section about Bézout domains in constructive mathematics, most of the text copied from principal ideal domain

   Anonymous

   diff, v3, current

2. • CommentRowNumber2.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 20th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadding a few examples of Bézout domains Anonymous <a href="https://ncatlab.org/nlab/revision/diff/B%C3%A9zout+domain/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/B%C3%A9zout+domain/3">v3</a>, <a href="https://ncatlab.org/nlab/show/B%C3%A9zout+domain">current</a>

   adding a few examples of Bézout domains

   Anonymous

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorGuest
   • CommentTimeMay 20th 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexOne thing I am currently unsure about: Are the integers $\mathbb{Z}$ a [[unique factorization domain]] in [[constructive mathematics]]? If so, then there exist [[Bézout domains]] that are unique factorization domains which are not [[principal ideal domains]]. Otherwise, $\mathbb{Z}$ is not a unique factorization domain in [[constructive mathematics]], and that fact should be added to the [[unique factorization domain]] article.

   One thing I am currently unsure about: Are the integers $\mathbb{Z}$ a unique factorization domain in constructive mathematics?

   If so, then there exist Bézout domains that are unique factorization domains which are not principal ideal domains. Otherwise, $\mathbb{Z}$ is not a unique factorization domain in constructive mathematics, and that fact should be added to the unique factorization domain article.

4. • CommentRowNumber4.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 20th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadding definition Anonymous <a href="https://ncatlab.org/nlab/revision/diff/B%C3%A9zout+domain/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/B%C3%A9zout+domain/3">v3</a>, <a href="https://ncatlab.org/nlab/show/B%C3%A9zout+domain">current</a>

   adding definition

   Anonymous

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorJ-B Vienney
   • CommentTimeJun 21st 2024
   • PermaLink
   Author: J-B Vienney
   Format: MarkdownItexAdded that every Bézout domain is a GCD domain. <a href="https://ncatlab.org/nlab/revision/diff/B%C3%A9zout+domain/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/B%C3%A9zout+domain/12">v12</a>, <a href="https://ncatlab.org/nlab/show/B%C3%A9zout+domain">current</a>

   Added that every Bézout domain is a GCD domain.

   diff, v12, current

6. • CommentRowNumber6.
   • CommentAuthornLab edit announcer
   • CommentTimeAug 19th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexchanged [[higher algebra - contents]] to [[algebra - contents]] in context sidebar Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/B%C3%A9zout+domain/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/B%C3%A9zout+domain/13">v13</a>, <a href="https://ncatlab.org/nlab/show/B%C3%A9zout+domain">current</a>

   changed higher algebra - contents to algebra - contents in context sidebar

   Anonymouse

   diff, v13, current