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.
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.
Related questions
Question
Prove that ring homomarphism
![Let R=Z and R'= set of all even integers. Then
%3D
(R', +, *) is a ring, where a * b
f:R→R' defined as f (a)
=
ab V a, beR'. The mapping
%3D
= 2a Va e R is a homomorphism.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c88a7ad-43ac-43e0-ba25-7b0eb62eedc4%2F514f2af8-d186-4136-992a-3d22e5af5a59%2Fckukio_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let R=Z and R'= set of all even integers. Then
%3D
(R', +, *) is a ring, where a * b
f:R→R' defined as f (a)
=
ab V a, beR'. The mapping
%3D
= 2a Va e R is a homomorphism.
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