Prove that ring homomarphism Let R=Z and R'= set of all even integers. Then%3D(R', +, *) is a ring, where a * bf:R→R' defined as f (a)=ab V a, beR'. The mapping%3D= 2a Va e R is a homomorphism.

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Answered: Let R=Z and R'= set of all even…

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 14E: 14. Let be a ring with unity . Verify that the mapping defined by is a homomorphism.

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Let R=Z and R'= set of all even integers. Then %3D (R', +, *) is a ring, where a* b= ab V a, be R'. The mapping f:R→R' defined as f (a) = 2a Va e R is a homomorphism.

Let R=Z and R'= set of all even integers. Then %3D (R', +, ) is a ring, where a b= ab V a, be R'. The mapping f:R→R' defined as f (a) = 2a Va e R is a homomorphism.