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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

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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?

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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  

 

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