Let be defined by Is a well-defined ring homomorphism? If so, find its kernel and image.
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Originally Posted by Maccaman 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??
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