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Let $\mathbb{F}$ be a field. I want to show that the ideal $\{ xg + yh \ | \ g, h ∈ \mathbb{F} [x, y] \}$ is not a principal ideal in $\mathbb{F}[x, y]$. Do I work by contradiction first, i.e. assume that it is principal?

Andrew Tawfeek
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Homaniac
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1 Answers1

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Yup, a proof by contradiction seems to be the right way to go. Suppose that it is principal. Show that $x, y \in I$. What does this tell you about the supposed generator? Why is this a contradiction?

4-ier
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