The module is injective iff it is a direct summand of an injective cogenerator

  • Thread starter ggugl
  • Start date
  • #1
ggugl
2
0
could any one give me a proof of this statment:

The module is injective iff it is a direct summand of an injective cogenerator.
 

Answers and Replies

  • #2
mathwonk
Science Advisor
Homework Helper
2020 Award
11,100
1,302
no, but for such things, see abelian categories by peter freyd.
 
Log in or register to reply now!

Related Threads on The module is injective iff it is a direct summand of an injective cogenerator

I Direct Products of Modules ... Canonical Injections ...
  • Last Post
Replies
12
Views
810
Demonstrating that a mapping is injective
  • Last Post
Replies
1
Views
1K
A Finding the injective hull
  • Last Post
Replies
5
Views
821
Ensuring injectivity of an operator
  • Last Post
Replies
10
Views
2K
Injection, surjection, and bijection
  • Last Post
Replies
4
Views
6K
I DimKer(T) = 0 <--> T is injective
  • Last Post
Replies
6
Views
1K
Show that linear transformation is surjective but not injective
  • Last Post
Replies
3
Views
6K
I Prove that if T is injective, T*T is invertible
  • Last Post
Replies
1
Views
332
Identity map and injectivity
  • Last Post
Replies
12
Views
6K
Bases, Invertibility and Injectivity Query
  • Last Post
Replies
2
Views
1K

Hot Threads

Recent Insights

Top