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

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 by a moderator: Oct 12, 2008