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Maximal Ideals, Residues and Ring Homomorphisms

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

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