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nLab > Latest Changes: locally free module

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2012
    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 8th 2012

    I wasn’t aware of proposition 1. Is it easy to see? I particularly want to get straight on the role of maximal ideals here as opposed to general prime ideals: I seem to recall a statement that a finitely generated module is projective iff its localization with respect to every prime ideal is free.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2012

    I am still fiddling with that a bit myself. See this MO discussion.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2012
    • (edited Oct 8th 2012)

    I think I have fixed now the obvious mistake and the less obvious one. Also at flat module. This should really be expanded on much further. I kind of regret now getting into it, because I need to focus on something else today. But maybe we can give a good comprehensive discussion of local freeness and the other conditions later.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 8th 2012

    Please focus on something else. I can wait.

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