Please write step by step, and clearly Theorem 8.3.14 (First Isomorphism Theorem) Let f be a homomorphism of a ring R into a ring R'. Thenf(R) is an ideal of R' andR/Ker f = f(R). ■

The given question is related with abstract algebra. Given the following theorem: (First Isomorphism…

Answered: Theorem 8.3.14 (First Isomorphism…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 47E

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Theorem 8.3.14 (First Isomorphism Theorem) Let f be a homomorphism of a ring R into a ring R'. Then f(R) is an ideal of R' and R/Ker f f(R).