Find all ring homomorphism from Z⊕Z into Z⊕Z

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milcah answered 1 year ago

Prove f: Zmod p---> Z mod p is a ring homomorphism and find the kernel of...

Prove f: Zmod p---> Z mod p is a ring homomorphism and find the kernel of f.

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Consider the ring homomorphism ϕ : Z[x] →R defined by ϕ(x) = √5. Let I = {f ∈Z[x]|ϕ(f) = 0}. First prove that I is an ideal in Z[x]. Then find g ∈ Z[x] such that I = (g). [You do not need to prove the last equality.]

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