Kindly answer correctly. Please show the necessary steps 15. Let R be a ring, I, J be ideals of R and f: R⇒ R/I x R/J be the function defined byf(a) = (a + I, a + J). Prove that f is a ring homomorphism and find its kernel

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Answered: 15. Let R be a ring, I, J be ideals of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 9E: 9. For any let denote in and let denote in . a. Prove that the mapping defined by is a...

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15. Let R be a ring, I, J be ideals of R and f: RR/I x R/J be the function defined by f(a) = (a + I,a+J). Prove that f is a ring homomorphism and find its kernel