Dgdrxrt

What defenses are there against being summoned by the Gate spell?

Do I have a twin with permutated remainders?

How much RAM could one put in a typical 80386 setup?

Add text to same line using sed

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I'm flying to France today and my passport expires in less than 2 months

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NMaximize is not converging to a solution

How does one intimidate enemies without having the capacity for violence?

Theorems that impeded progress

What does the "remote control" for a QF-4 look like?

Approximately how much travel time was saved by the opening of the Suez Canal in 1869?

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strTok function (thread safe, supports empty tokens, doesn't change string)

How much of data wrangling is a data scientist's job?

Does detail obscure or enhance action?

Character reincarnated...as a snail

Why doesn't H₄O²⁺ exist?

If human space travel is limited by the G force vulnerability, is there a way to counter G forces?

Can a Cauchy sequence converge for one metric while not converging for another?

Are the number of citations and number of published articles the most important criteria for a tenure promotion?

Why does Kotter return in Welcome Back Kotter?

Can you really stack all of this on an Opportunity Attack?

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Confusion About Invertible Modules

Finitely generated projective modules are locally freeAre projective modules over an artinian ring free?The existence of a projective resolution of M from finite rank free modulesHartshorne Chapter II exercise 5.7 on Invertible sheavesProjectivity of a (prime) ideal in a noetherian integral domainEvery finitely generated flat module over a ring with a finite number of minimal primes is projectiveQuotient of free modules is torsion implies rank is the same?Computing Picard groups by showing invertible modules are uniquely determinedInvertible ideals and locally free moduleThe multiplication of rank for finite projective modules

-1

$begingroup$

According to the Stacks Project, a module is invertible iff it is locally free of rank one.(In the strong sense, not just that the stalks are free).Link

So, according to this link, the module is finite projective of rank one. But this question says that this is not true. What is the correct answer here?

commutative-algebra projective-module

share|cite|improve this question

asked Mar 29 at 11:46

Jehu314Jehu314

1549

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can you spell out the place where "this question" says that this is not true?
  $endgroup$
  – Youngsu
  Mar 29 at 14:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It says that condition 1) is strictly stronger.
  $endgroup$
  – Jehu314
  Mar 29 at 15:03
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is your argument? It is better for the readers if you state the necessary statements in your post and specify your question explicitly.
  $endgroup$
  – Youngsu
  Mar 29 at 17:56
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Finiteness is the difference as stated in those two links.
  $endgroup$
  – Youngsu
  Mar 29 at 18:31
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is your question? Are you asking whether a locally free module of rank $1$ is projective?
  $endgroup$
  – Qiaochu Yuan
  Mar 29 at 19:48
  

  
  
  
  

 | 
show 6 more comments

-1

$begingroup$

According to the Stacks Project, a module is invertible iff it is locally free of rank one.(In the strong sense, not just that the stalks are free).Link

So, according to this link, the module is finite projective of rank one. But this question says that this is not true. What is the correct answer here?

commutative-algebra projective-module

share|cite|improve this question

asked Mar 29 at 11:46

Jehu314Jehu314

1549

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can you spell out the place where "this question" says that this is not true?
  $endgroup$
  – Youngsu
  Mar 29 at 14:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It says that condition 1) is strictly stronger.
  $endgroup$
  – Jehu314
  Mar 29 at 15:03
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is your argument? It is better for the readers if you state the necessary statements in your post and specify your question explicitly.
  $endgroup$
  – Youngsu
  Mar 29 at 17:56
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Finiteness is the difference as stated in those two links.
  $endgroup$
  – Youngsu
  Mar 29 at 18:31
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is your question? Are you asking whether a locally free module of rank $1$ is projective?
  $endgroup$
  – Qiaochu Yuan
  Mar 29 at 19:48
  

  
  
  
  

 | 
show 6 more comments

$begingroup$

According to the Stacks Project, a module is invertible iff it is locally free of rank one.(In the strong sense, not just that the stalks are free).Link

So, according to this link, the module is finite projective of rank one. But this question says that this is not true. What is the correct answer here?

commutative-algebra projective-module

share|cite|improve this question

asked Mar 29 at 11:46

Jehu314Jehu314

1549

$endgroup$

share|cite|improve this question

asked Mar 29 at 11:46

Jehu314Jehu314

1549

share|cite|improve this question

asked Mar 29 at 11:46

Jehu314Jehu314

1549

asked Mar 29 at 11:46

Jehu314Jehu314

1549

asked Mar 29 at 11:46

Jehu314Jehu314

1549