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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 29th 2012
    • (edited Sep 23rd 2012)

    started projective module

    (will need to move some material around with projective object. Also, I am splitting off now projective resolution from resolution )

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2012
    • (edited Sep 23rd 2012)

    I have been expanding the Properties-section at projective module. Made fully explicit in detailed proofs what was previously just alluded to as “clearly”: that every direct summand of a free module is projective, assuming the axiom of choice. This is meant to be expository and serve newbies.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 17th 2012
    • (edited Oct 17th 2012)

    added a section Definition - F-resolutions of an object.

    Will now add a corresponding Properties-section…

    (Sorry, this should go to the thread on projective resolution…)

  1. Added to projective module the many ways to characterize finitely generated projective modules.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2016
    • (edited Jul 11th 2016)

    For completeness, I have added to the beginning of the entry the elementary proof of the first claim, here.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2016
    • (edited Jul 26th 2016)

    projective module, Prop. 5 number 4:

    There exist elements x 1,,x nPx_1,\ldots,x_n \in P and linear forms ϑ 1,,ϑ nHom(P,R)\vartheta_1,\ldots,\vartheta_n \in Hom(P,R) such that x= iϑ i(x)x ix = \sum_i \vartheta_i(x) x_i for all xPx \in P.

    In my memory, these data were called a normal basis of the projective module ?

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