The discussion revolves around the concept of homomorphisms, specifically the mapping of the kernel of a homomorphism from set A to set B. Participants explore the implications of defining a new map from the kernel to B and the nature of the image of this mapping.
Participants express differing views on the significance of the mapping from the kernel to B, with some finding it trivial while others see value in the exploration of the concept. The discussion does not reach a consensus on the importance of this mapping.
There are unresolved questions regarding the implications of the kernel mapping and the nature of the identity map in this context. Some participants also struggle with formatting issues related to LaTeX, which may affect the clarity of their contributions.
You need to close the tex enviroment. e.g.tgt said:Suppose there exists a homomorphism f:A->B then does it make sense to have
why doesn't my tex show up?
Offcourse, Im(f_{Ker(f)})=1_{B}
[tex]\frac{dy}{dx}[ /tex]morphism said:What are you trying to say?
Yes, that makes sense. It isn't very interesting, however, since [itex]f_{Ker(f)}[/itex] is just the identity map f(x)= 1B, as you say.tgt said:Suppose there exists a homomorphism f:A->B then does it make sense to have
[tex]f_{Ker(f)}:Ker(f) \to B[/tex] ?
why doesn't my tex show up?
Offcourse, [tex]Im(f_{Ker(f)})=1_{B}[/tex]
Moderator Note: [/color]Fixed LaTeX.