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Let F be field. Let f: F[x] -> F the map that sends every polynomial to the sum of its coefficients.

Let F be field. Let f: F[x] -> F the map that sends every polynomial to the sum of its coefficients.

  • Prove that f is a ring homomorphism and describe its kernel
  • Prove that Ker f = <x-1>
  • Use item (b) to prove that F[x]/ker f = F
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8932276yhed10.doc

a Let F be field and let f : F x F Let f be a homomorphism of a ring R into a integral domain R
Then kernel f
I f x : x R and x 0 R Since I f R, therefore there exists an element a R such that a a...

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