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- Krull's_principal_ideal_theorem abstract "In commutative algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a Noetherian ring. The theorem is sometimes referred to by its German name, Krulls Hauptidealsatz (Satz meaning "proposition" or "theorem").Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.This theorem can be generalized to ideals that are not principal, and the result is often called Krull's height theorem. This says that if R is a Noetherian ring and I is a proper ideal generated by n elements of R, then I has height at most n.The principal ideal theorem and the generalization, the height theorem, both follow from the fundamental theorem of dimension theory. Bourbaki's Commutative Algebra gives a direct proof. Kaplansky's Commutative ring includes a proof due to David Rees.".
- Krull's_principal_ideal_theorem wikiPageID "542421".
- Krull's_principal_ideal_theorem wikiPageRevisionID "593406757".
- Krull's_principal_ideal_theorem hasPhotoCollection Krull's_principal_ideal_theorem.
- Krull's_principal_ideal_theorem subject Category:Commutative_algebra.
- Krull's_principal_ideal_theorem subject Category:Ideals.
- Krull's_principal_ideal_theorem subject Category:Theorems_in_algebra.
- Krull's_principal_ideal_theorem type Abstraction100002137.
- Krull's_principal_ideal_theorem type Cognition100023271.
- Krull's_principal_ideal_theorem type Communication100033020.
- Krull's_principal_ideal_theorem type Content105809192.
- Krull's_principal_ideal_theorem type Idea105833840.
- Krull's_principal_ideal_theorem type Ideal105923696.
- Krull's_principal_ideal_theorem type Ideals.
- Krull's_principal_ideal_theorem type Message106598915.
- Krull's_principal_ideal_theorem type Proposition106750804.
- Krull's_principal_ideal_theorem type PsychologicalFeature100023100.
- Krull's_principal_ideal_theorem type Statement106722453.
- Krull's_principal_ideal_theorem type Theorem106752293.
- Krull's_principal_ideal_theorem type TheoremsInAlgebra.
- Krull's_principal_ideal_theorem comment "In commutative algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a Noetherian ring.".
- Krull's_principal_ideal_theorem label "Krull's principal ideal theorem".
- Krull's_principal_ideal_theorem label "Teorema dell'ideale principale".
- Krull's_principal_ideal_theorem label "Théorème des idéaux principaux de Krull".
- Krull's_principal_ideal_theorem sameAs Théorème_des_idéaux_principaux_de_Krull.
- Krull's_principal_ideal_theorem sameAs Teorema_dell'ideale_principale.
- Krull's_principal_ideal_theorem sameAs m.02n9xp.
- Krull's_principal_ideal_theorem sameAs Q3527241.
- Krull's_principal_ideal_theorem sameAs Q3527241.
- Krull's_principal_ideal_theorem sameAs Krull's_principal_ideal_theorem.
- Krull's_principal_ideal_theorem wasDerivedFrom Krull's_principal_ideal_theorem?oldid=593406757.
- Krull's_principal_ideal_theorem isPrimaryTopicOf Krull's_principal_ideal_theorem.