# Idea question

## Homework Statement

Why are prime ideals so important?

## The Attempt at a Solution

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2) Because they correspond to irreducible curves in geometry. For example, the curve y=x2 is irreducible, and indeed, the ideal (y-x2) is prime in $\mathbb{C}[x,y]$. On the other, the curve xy=0 is not irreducible since it exists out of the pieces x=0 and y=0. And indeed, the ideal (xy) is not prime.