Krull's theorem
= Krull's theorem
{wiki=Krull's_theorem}
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 \\).