Thread: Well-defined, surjective ring homomorphism.

Hey guys.

I have a commutative ring R, with two ideals, I and J, in R, where I J.
Now I have to show that given by is a well defined, surjective ring homomorphism.

Right now I cant even figure out what i need to do, to prove that it is well-defined. I'm missing parts of what I should have learned, but as far as I've been able to figure out, a homomorphism is well-defined when for any , .
But I can't figure out how to prove that. If someone could give me a hint, I would really appreciate it. Perhaps I need a more stringent definition of "well-defined" or if you could give me an example of a proof kind of like mine?

All help is appreciated.
Morten

Originally Posted by m112358

Right now I cant even figure out what i need to do, to prove that it is well-defined.

We have to prove that does not depend on the representative element . If then that is , and as a consequence .

Arh ok, now I understand. Alright, that was simple, guess I had been staring too blindly to notice. Thanks for the help

Morten