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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning