Prove that $I=(xy-1)$ is prime but not maximal in $\mathbb{C}[x,y]$. Prove also that $\mathbb{C}[x,y]/I$ has infinitely many prime ideals. I must prove that the quotient Ring is an Integral domain and not a Field. No idea whatsoever. Any help please.
2026-04-03 23:19:04.1775258344
Prime ideals in $\mathbb{C}[x,y]$
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