Given R=all non-zero real numbers.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Abstract Algebra question?

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