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Prove that the ideal $\left \langle x,y\right\rangle\subseteq\mathbb{C}[x,y]$ can be shown as $\bigcup_{i\in I}Q_i$ such that $Q_i$ is a prime ideal.

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  • $\begingroup$ $\Bbb C[x,y]$ is the polynomial ring with two indeterminates? $\endgroup$ – Bernard Mar 22 at 16:10
  • $\begingroup$ @Bernard Indeed. $\endgroup$ – J. Doe Mar 22 at 16:11
  • $\begingroup$ Well, $\langle x,y\rangle$ itself is a maximal ideal. $\endgroup$ – Bernard Mar 22 at 16:12

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