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

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.

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