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Krull's theorem

 Home Mathematics Fields of mathematics Fields of abstract algebra Ring theory Ideals (ring theory)
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Krull's theorem is a result in commutative algebra that pertains to the structure of integral domains, specifically regarding the heights of prime ideals in a Noetherian ring. The theorem states: In a Noetherian ring (or integral domain), the height of a prime ideal \( P \) is less than or equal to the number of elements in any generating set of the ideal \( P \).

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