(a) Assume R is commutative. Prove that if P is a prime ideal of R and Pcontains no zero divisors then R is an integral domain.(b) Let R be the ring of all continuous functions from [0, 1] to R and foreach c E [0, 1] let ø be the evaluation map at c from R to R. Whatis the kernel of o? Is ker p a maximal ideal of R? (Explain)

Note: Here we are solving problem (a) for problem (b) please submit the question again. Given: Let R…

Answered: R is an integral domain.

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R is an integral domain.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 17E

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(a) Assume R is commutative. Prove that if P is a prime ideal of R and P
contains no zero divisors then R is an integral domain.
(b) Let R be the ring of all continuous functions from [0, 1] to R and for
each c E [0, 1] let ø be the evaluation map at c from R to R. What
is the kernel of o? Is ker p a maximal ideal of R? (Explain)

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