Define the mapping 7: R²→R by π((x,y))=x. (Note that R is a group under addition with identity 0). Prove that is a homomorphism. Find the kernel of T. a) b)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 29E
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Define the mapping 7: R²→R by π((x,y))=x.
(Note that R is a group under addition with identity 0).
Prove that is a homomorphism.
Find the kernel of T.
a)
b)
Transcribed Image Text:Define the mapping 7: R²→R by π((x,y))=x. (Note that R is a group under addition with identity 0). Prove that is a homomorphism. Find the kernel of T. a) b)
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