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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 29th 2012
   • (edited Sep 23rd 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted _[[projective module]]_ (will need to move some material around with _[[projective object]]_. Also, I am splitting off now _[[projective resolution]]_ from _[[resolution]]_ )

   started projective module

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

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 23rd 2012
   • (edited Sep 23rd 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 17th 2012
   • (edited Oct 17th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a section _[Definition - F-resolutions of an object](http://ncatlab.org/nlab/show/projective+resolution#FResolutions)_. Will now add a corresponding Properties-section... (Sorry, this should go to the thread on [[projective resolution]]...)

   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…)

4. • CommentRowNumber4.
   • CommentAuthorIngoBlechschmidt
   • CommentTimeMay 8th 2015
   • PermaLink
   Author: IngoBlechschmidt
   Format: MarkdownItexAdded to _[[projective module]]_ the many ways to characterize finitely generated projective modules.

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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2016
   • (edited Jul 11th 2016)
   • PermaLink
   Author: Urs
   Format: MarkdownItexFor completeness, I have added to the beginning of the entry the elementary proof of the first claim, [here](https://ncatlab.org/nlab/show/projective+module#NProjectiveIFFHomNExact).

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

6. • CommentRowNumber6.
   • CommentAuthorzskoda
   • CommentTimeJul 26th 2016
   • (edited Jul 26th 2016)
   • PermaLink
   Author: zskoda
   Format: MarkdownItex[[projective module]], Prop. 5 number 4: > There exist elements $x_1,\ldots,x_n \in P$ and linear forms $\vartheta_1,\ldots,\vartheta_n \in Hom(P,R)$ such that $x = \sum_i \vartheta_i(x) x_i$ for all $x \in P$. In my memory, these data were called a _normal basis_ of the projective module ?

   projective module, Prop. 5 number 4:

   There exist elements $x_1,\ldots,x_n \in P$ and linear forms $\vartheta_1,\ldots,\vartheta_n \in Hom(P,R)$ such that $x = \sum_i \vartheta_i(x) x_i$ for all $x \in P$.

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