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
11,307
1,522
no, but for such things, see abelian categories by peter freyd.
 

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

Demonstrating that a mapping is injective
  • Last Post
Replies
1
Views
1K
P
I Direct Products of Modules ... Canonical Injections ...
  • Last Post
Replies
12
Views
1K
Math Amateur
Injective Mapping
  • Last Post
Replies
3
Views
2K
A
I DimKer(T) = 0 <--> T is injective
  • Last Post
Replies
6
Views
2K
fresh_42
A Finding the injective hull
  • Last Post
Replies
5
Views
954
M
B Surjective/injective operators
  • Last Post
Replies
7
Views
1K
W
Injective linear tranformations
  • Last Post
Replies
3
Views
4K
H
Linear injective mapping
  • Last Post
Replies
6
Views
5K
S
I Prove that if T is injective, T*T is invertible
  • Last Post
Replies
1
Views
719
B
Show that linear transformation is surjective but not injective
  • Last Post
Replies
3
Views
6K
conquest

Hot Threads

Recent Insights

Top