- #1
raj123
- 16
- 0
Given R=all non-zero real numbers.
I have a mapping Q: R-> R defined by Q(a) = a^4 for a in R. I have to show that Q is a homomorphism from (R, .) to itself and then find kernel of Q.
In order to prove homomorphism i did this, for all a, b in R
Q(ab) = (ab)^4 = a^4b^4 = Q(a)Q(b).
Is this correct way? Also how do i find the kernel of Q.
thanks
I have a mapping Q: R-> R defined by Q(a) = a^4 for a in R. I have to show that Q is a homomorphism from (R, .) to itself and then find kernel of Q.
In order to prove homomorphism i did this, for all a, b in R
Q(ab) = (ab)^4 = a^4b^4 = Q(a)Q(b).
Is this correct way? Also how do i find the kernel of Q.
thanks