Re: Isomorphism of quotient ring

On May 5, 12:39 pm, Jose <jose.fra...@xxxxxxxxx> wrote:
Do you mean is to show that the map g:K[x,y,z]/(...) ->k[t]
by g(x)=t...

and the map f:K[t]-> k[x,y,z]/(..)

but f(t)= ?? is it f(t)=x, f(t^2)=y, f(t^3)=z ?

Is that correct ?

What I mean is the following: you have a map

g:k[x,y,z] -> k[t]

such that

g(x)=t,
g(y)=t^2,
g(z)=t^3.

Can you see whether g induces a map

h : k[x,y,z]/(x^2-y,x^3-z,y^3-z^2) --> k[t]

?

Can you describe a map

f : k[t] --> k[x,y,z]/(x^2-y,x^3-z,y^3-z^2)

such that

f h = id
h f = id

?

-- m
.