# Does this make sense?

1. Oct 9, 2008

### tgt

Suppose there exists a homomorphism f:A->B then does it make sense to have

$$f_{Ker(f)}:Ker(f) \to B$$ ?

why doesn't my tex show up?

Offcourse, $$Im(f_{Ker(f)})=1_{B}$$

Moderator Note: Fixed LaTeX.

Last edited: Oct 10, 2008
2. Oct 9, 2008

### Hootenanny

Staff Emeritus
You need to close the tex enviroment. e.g.
Code (Text):
[tex]\frac{dy}{dx}[ /tex]
(without the space in the square brackets of course)

Last edited: Oct 9, 2008
3. Oct 9, 2008

### morphism

What are you trying to say?

4. Oct 9, 2008

### daveyinaz

Are you trying to say that the elements in A that are in the kernel map into B. Well yes that's true since they all map to the zero element within B.

5. Oct 10, 2008

### tgt

Given a map, we can define a new map, mapping the kernel of the map to the range of the map.

6. Oct 10, 2008

### morphism

Yes, but what's the point?

7. Oct 10, 2008

### HallsofIvy

Staff Emeritus
Yes, that makes sense. It isn't very interesting, however, since $f_{Ker(f)}$ is just the identity map f(x)= 1B, as you say.

Last edited: Oct 12, 2008