I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and Affine Algebraic Sets, Example 3 on page 660 reads as follows: (see attachment)
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Let in .
If is an element of V, then .
If , then also and we can write .
It follows that V is the set .
For any polynomial . we can write
... ... ... etc etc
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I cannot follow the line of reasoning:
"For any polynomial . we can write "
Can anyone clarify why this is true and why D&F are taking this step?
Peter