# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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 $x_1,\ldots,x_n \in P$ 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 ?

• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)