Idea question

  • #1

Homework Statement



Why are prime ideals so important?

Homework Equations





The Attempt at a Solution

 
Last edited:

Answers and Replies

  • #2
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Hi Metric_Space :smile:

1) Because they form a generalization for prime numbers, and prime numbers are important.
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 [itex]\mathbb{C}[x,y][/itex]. 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.
 

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