= Krull's principal ideal theorem
{wiki=Krull's_principal_ideal_theorem}
Krull's Principal Ideal Theorem is a significant result in commutative algebra that connects the concept of prime ideals to the structure of a ring. Specifically, it provides conditions under which a principal ideal generated by an element in a Noetherian ring intersects non-trivially with a prime ideal. The theorem states the following: Let \\( R \\) be a Noetherian ring, and let \\( P \\) be a prime ideal of \\( R \\).
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