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    Maximal Ideals, Residues and Ring Homomorphisms

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    Let . Show that the map the residue of a+ b modulo 2, is a ring homomorphism with . Prove that . Hence, or otherwise, give a maximal ideal of .
    Consider the ideal (2)+(x) of . Show that (2)+(x) . Hence explain why (x) is not a maximal ideal of .

    NOTE: All question marks are Z, the integers

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    https://brainmass.com/math/ring-theory/maximal-ideals-residues-ring-homomorphisms-54473

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    1. Proof:
    For any , we have

    Here we use the fact that in ...

    Solution Summary

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

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