Mar 30, 2012 Thread starter #1 S 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?

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?

Mar 30, 2012 Moderator #2 Opalg MHB Oldtimer Staff member Feb 7, 2012 2,725 StefanM said: Is this correct? Click to expand... Yes.