Let be defined by Is a well-defined ring homomorphism? If so, find its kernel and image.
yes it is and the kernel is (0). the easiest way to see this is to just check 3 elements of and see that iff also you need to check that which is because
in the image is (here by 0 i mean the coset and by 2 i mean etc.)
Thank-you for your help, but I'm still confused because I'm getting things mixed up. I'm having trouble seeing that is a well-defined ring homomorphism to start with. Could you show me why it is??