I think I have to proceed by contradiction, but I don't know how to do it. Any suggestion?
Thanks for your help.
2026-04-13 19:46:13.1776109573
Show that ideal $(X,Y)\subset \mathbb{R}[X,Y]$ is not invertible
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Hint: If it were invertible, it would be a projective ideal, hence its localisations at every maximal ideal would be free and thus principal.