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    Ring Homomorphisms, Residues and Distinct Maximal Ideals

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    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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    https://brainmass.com/math/ring-theory/ring-homomorphisms-residues-distinct-maximal-ideals-54471

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    1. Proof:
    Since is a ring, then for any , we have (mod ) (mod ) (mod ). (mod ) (mod ) (mod ). Thus for any , ...

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

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