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Math Help - Generated Ideals

  1. #1
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    Generated Ideals

    Does <1>=<1+x,1+y> in \mathbb{Q}[x,y]?

    I don't think this is true, how would I go about showing it?
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  2. #2
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    Quote Originally Posted by skamoni View Post
    Does <1>=<1+x,1+y> in \mathbb{Q}[x,y]?

    I don't think this is true, how would I go about showing it?

    Suppose it is \Longrightarrow f(x,y)(1+x)+g(x,y)(1+y)=1 , for some f,g\in \mathbb{Q}[x,y] . Now apply the evaluation homomorphism x\mapsto -1\,,\,\,y\mapsto -1 to this equality and get a contradiction.

    Tonio
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