Re: Isomorphism of quotient ring

On May 5, 3:50 am, Jose <jose.fra...@xxxxxxxxx> wrote:
I was thinking of using the isomorphism theorem, by let
g:k[x,y,z] -> k[t]
g(x)=t,g(y)=t^2, g(z)=t^3

and then I was hoping to have ker(g)=(x^2-y,x^3-z,y^3-z^2)

Is this the right way to start?

Because proofing this the kernel is not that much clear, can you just tell me if my way is correct or not?

That is quite correct.

Instead of checking that that is the kernel, you
can find an inverse isomorphism...

-- m
.