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Let I be an ideal of the ring R. Prove that the reduction map R[x] →...

Let I be an ideal of the ring R. Prove that the reduction map R[x] → (R/I)[x] is a ring homomorphism.

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Answer #1

Define a map

where is the coset of in .

Now claim that f is ring homomorphism .

(1) f is well defined function :

Suppose that

(2) Ring homomorphism :-

f is ring homomorphism.

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