PlanetMath: Krull intersection theorem

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Krull intersection theorem

(Theorem)

Given a Noetherian ring , an -module , and an ideal inside the radical of , we have that is separated with respect to the -adic topology.

Furthermore, if is also an integral domain and $J\subset A$ is a proper ideal, we have

$\displaystyle \bigcap_{n>0}J^n=(0)$

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Cross-references: proper ideal, integral domain, topology, separated, radical, ideal, noetherian ring
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This is version 4 of Krull intersection theorem, born on 2004-09-14, modified 2008-05-27.
Object id is 6173, canonical name is KrullIntersectionTheorem.
Accessed 1665 times total.

Classification:

13E05 (Commutative rings and algebras :: Chain conditions, finiteness conditions :: Noetherian rings and modules)

Pending Errata and Addenda

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