Abstract Algebra - Homomorphisms...
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Abstract Algebra - Homomorphisms...

[From: ] [author: ] [Date: 12-03-11] [Hit: ]
f(1) = 1/2, and for any a, b in Z, f(a+b) = (a+b)/2 = a/2 + b/2 = f(a) + f(b).2) Define g : Z → Q by g(n) = 0 for all n.I hope this helps!......
1) Give an example of a map from Z to Q that is a homomorphism for which 1 in Z is neither mapped to 1 nor -1 in Q (operation in Z and Q is addition)

2) Construct a homomorphism from Z to Q that is not an injection.

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1) Define f : Z → Q by f(n) = n/2.
Then, f(1) = 1/2, and for any a, b in Z, f(a+b) = (a+b)/2 = a/2 + b/2 = f(a) + f(b).
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2) Define g : Z → Q by g(n) = 0 for all n.

I hope this helps!
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keywords: Homomorphisms,Abstract,Algebra,Abstract Algebra - Homomorphisms...
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