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Math Help - Algebraic set

  1. #1
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    Algebraic set

    Show that \phi : K \rightarrow K^3 given by \phi(t) = (t,f(t),g(t)) with f,g \in K[x] is an algebraic set of K^3
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  2. #2
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    Quote Originally Posted by roporte View Post
    Show that \phi : K \rightarrow K^3 given by \phi(t) = (t,f(t),g(t)) with f,g \in K[x] is an algebraic set of K^3
    let p(x,y,z)=y -f(x), \ q(x,y,z)=z-g(x). clearly both p(x,y,z) and q(x,y,z) are in K[x,y,z] and the image of \phi is the solutions of the system: p(x,y,z)=0, \ q(x,y,z)=0. \ \ \Box
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