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Define e : Z6 -+ Z3 by e([a]6) = [ah for each [a]6 E Z6.(a) Prove that e is well
Chapter 21, Problem 21.5(choose chapter or problem)
QUESTION:
Define e : Z6 -+ Z3 by e([a]6) = [ah for each [a]6 E Z6.(a) Prove that e is well defined.(b) Prove that e is a homomorphism.(c) What is Ker e?
Questions & Answers
QUESTION:
Define e : Z6 -+ Z3 by e([a]6) = [ah for each [a]6 E Z6.(a) Prove that e is well defined.(b) Prove that e is a homomorphism.(c) What is Ker e?
ANSWER:Step 1 of 3
Define by
Then prove
(a) is well defined.
First, note that is well defined function, since if in, then and this implies that since
Thus, and so