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Homomorphism of rings

StefanM

New member
Jan 30, 2012
28
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?
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,725