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Ring Homomorphisms, Residues and Distinct Maximal Ideals

Let . Prove that the map given by , where is the residue of a modulo n, is a ring homomorphism. Find the kernel and image of .

Prove that if is a ring homomorphism, then given by is also a ring homomorphism.

Write down two distinct maximal ideals of . Does have a finite or infinite number of maximal ideals? Give brief reasons for your answer.

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Ring Homomorphisms, Residues and Distinct Maximal Ideals are investigated. The solution is detailed and well presented.

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