Let's assume that is a ring, which operations are addition and multiplication using components (eg. ). The task is to prove that x-axis and y-axis are ideals of this ring. Following theorem must be used in the proof:
"Ring homomorphism's kernel is 's ideal".
I think the problem isn't very hard, when the correct homomorphism is found. I tried some, but I couldn't discover anything that works. So, any help is welcome. Thank you very much!