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nLab > Latest Changes: Euclidean domain

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 2nd 2015

    I’m losing track of all the little recent edits I’ve made, but among them I created Euclidean domain, and added to principal ideal domain and unique factorization domain, proving the familiar inclusions between them. Piddled around a little with polynomial as well.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 19th 2020

    Added a description of the Euclidean algorithm.

    diff, v7, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeMay 2nd 2022
    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeMay 2nd 2022

    If every Euclidean domain is a principal ideal domain in constructive mathematics, does that mean that the integers are not an Euclidean domain? Because according to the principal ideal domain article, the integers aren’t a principal ideal domain.

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeMay 2nd 2022

    This mathoverflow thread shows that every Euclidean domain is a unique factorization domain, avoiding principal ideal domains entirely, but I’m not sure if the proof is valid constructively.

    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeMay 2nd 2022
    There is also of course the question of how your integral domain is defined: is the inequality a denial inequality or a tight apartness relation?
    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeMay 2nd 2022

    The usual definition of unique factorization domain doesn’t seem to be constructively valid, see this Mathoverflow post.

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

    Anonymouse

    diff, v17, current

1 to 8 of 8

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