MHB Homomorphism of Rings & Is Map f:C->Z a Homo?

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The discussion centers on determining whether the map f:C->Z defined by f(a+bi)=a is a homomorphism of rings. It is established that while f(x+y)=f(x)+f(y) holds true, f(xy) does not equal f(x)f(y), indicating that the map fails to satisfy the necessary conditions for a homomorphism. Therefore, the conclusion is that the map is not a homomorphism of rings. The participants confirm the correctness of this analysis. The discussion effectively clarifies the properties required for ring homomorphisms.
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I'm trying to see if the map f:C->Z,f(a+bi)=a is a homomorphism of rings.
Let x=a+bi and y=c+di...then f(x+y)=a+c=f(x)+f(y) but f(xy)=f((ac-db)+(ad+bc)i)=ac-db/= f(x)f(y)...so the map is not a homomorphism of rings.
Is this correct?
 
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StefanM said:
Is this correct?
Yes. (Smile)
 
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