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- Krulls_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.".
- Krulls_principal_ideal_theorem wikiPageExternalLink supDim.pdf.
- Krulls_principal_ideal_theorem wikiPageID "542421".
- Krulls_principal_ideal_theorem wikiPageLength "1494".
- Krulls_principal_ideal_theorem wikiPageOutDegree "13".
- Krulls_principal_ideal_theorem wikiPageRevisionID "649672322".
- Krulls_principal_ideal_theorem wikiPageWikiLink Category:Commutative_algebra.
- Krulls_principal_ideal_theorem wikiPageWikiLink Category:Ideals.
- Krulls_principal_ideal_theorem wikiPageWikiLink Category:Theorems_in_abstract_algebra.
- Krulls_principal_ideal_theorem wikiPageWikiLink Commutative_algebra.
- Krulls_principal_ideal_theorem wikiPageWikiLink David_Rees_(mathematician).
- Krulls_principal_ideal_theorem wikiPageWikiLink Dimension_theory_(algebra).
- Krulls_principal_ideal_theorem wikiPageWikiLink Height_(ring_theory).
- Krulls_principal_ideal_theorem wikiPageWikiLink Ideal_(ring_theory).
- Krulls_principal_ideal_theorem wikiPageWikiLink Krull_dimension.
- Krulls_principal_ideal_theorem wikiPageWikiLink Noetherian_ring.
- Krulls_principal_ideal_theorem wikiPageWikiLink Principal_ideal.
- Krulls_principal_ideal_theorem wikiPageWikiLink Satz_(disambiguation).
- Krulls_principal_ideal_theorem wikiPageWikiLink Wolfgang_Krull.
- Krulls_principal_ideal_theorem wikiPageWikiLink Éléments_de_mathématique.
- Krulls_principal_ideal_theorem wikiPageWikiLinkText "''Hauptidealsatz''".
- Krulls_principal_ideal_theorem wikiPageWikiLinkText "Krull's Hauptidealsatz".
- Krulls_principal_ideal_theorem wikiPageWikiLinkText "Krull's height theorem".
- Krulls_principal_ideal_theorem wikiPageWikiLinkText "Krull's principal ideal theorem".
- Krulls_principal_ideal_theorem hasPhotoCollection Krulls_principal_ideal_theorem.
- Krulls_principal_ideal_theorem wikiPageUsesTemplate Template:Citation.
- Krulls_principal_ideal_theorem subject Category:Commutative_algebra.
- Krulls_principal_ideal_theorem subject Category:Ideals.
- Krulls_principal_ideal_theorem subject Category:Theorems_in_abstract_algebra.
- Krulls_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.".
- Krulls_principal_ideal_theorem label "Krull's principal ideal theorem".
- Krulls_principal_ideal_theorem sameAs Théorème_des_idéaux_principaux_de_Krull.
- Krulls_principal_ideal_theorem sameAs Teorema_dellideale_principale.
- Krulls_principal_ideal_theorem sameAs クルルの単項イデアル定理.
- Krulls_principal_ideal_theorem sameAs 크룰_높이_정리.
- Krulls_principal_ideal_theorem sameAs m.02n9xp.
- Krulls_principal_ideal_theorem sameAs Q3527241.
- Krulls_principal_ideal_theorem sameAs Q3527241.
- Krulls_principal_ideal_theorem wasDerivedFrom Krulls_principal_ideal_theoremoldid=649672322.
- Krulls_principal_ideal_theorem isPrimaryTopicOf Krulls_principal_ideal_theorem.