Give an example with justification of a function f:R1-->R2,where(R1,+,.) and (R2,+,.) are rings and such that f:(R1,+)-->(R2,+) is a group homomorphism but f is not a ring homomorphism.?
1 Answer
Jul 17, 2018
Explanation:
Consider
We find:
#f(hat(0)) = hat(2) * hat(0) = hat(0)#
#f(a+b) = hat(2) * (a+b) = hat(2) * a+hat(2) *b = f(a)+f(b)#
but:
#f(hat(1) * hat(1)) = hat(2) * (hat(1) * hat(1)) = hat(2) != hat(1) = (hat(2) * hat(1)) * (hat(2) * hat(1)) = f(hat(1)) * f(hat(1))#