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.