Let m be a fixed positive integer. For any integer a, let a denote a mod m. Show that the mapping of ø: Z[x] → Zm[x] given by 6(a„x" + a,-"-1 + · .. + a) = a" + ā,-j"-1+ . . . + āo is a ring homomorphism.

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Q: {{: "]ancez}. - Let R = Prove or disprove that the map- a b ping → a is a ring homomorphism.

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Q: 1. Let R be a ring with the additive identity 0. Prove that for any a E R, 0- a = 0.

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Q: Show the map f : Q[x] → Q(√3) defined by f(p(x)) = p(√3) is a ring homomorphism. FInd its kernel.

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Q: don't understand how phi(a+c)=a+c. Please explain. Thank you

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