5. Let R be a commutative ring with identity. Let f: R[x] -f(p(x)) = E, ai, where p(x) = ao+a1x + a2x² + ... + amx™m. Prove that f isa homomorphism of rings. Notice that f(p(x)) = p(1), where 1 = 1R E R.→ R be defined by4 4. Risc

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Answered: 5. Let R be a commutative ring with…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 35E: Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a...

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5. Let R be a commutative ring with identity. Let f: R[x] → R be defined by f(p(x)) = Eo ai, where p(x) = ao + a1x+ a2r² +... a homomorphism of rings. Notice that f(p(x)) = p(1), where 1 = 1R E R. + amx. Prove that f is