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- Krull_dimension abstract "In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.The Krull dimension has been introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal I in a polynomial ring R is the Krull dimension of R/I.A field k has Krull dimension 0; more generally, k[x1, ..., xn] has Krull dimension n. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.".
- Krull_dimension wikiPageID "56079".
- Krull_dimension wikiPageLength "9869".
- Krull_dimension wikiPageOutDegree "66".
- Krull_dimension wikiPageRevisionID "674573693".
- Krull_dimension wikiPageWikiLink Affine_variety.
- Krull_dimension wikiPageWikiLink Algebraic_geometry.
- Krull_dimension wikiPageWikiLink Annihilator_(ring_theory).
- Krull_dimension wikiPageWikiLink Artinian_ring.
- Krull_dimension wikiPageWikiLink Associated_graded_ring.
- Krull_dimension wikiPageWikiLink Cambridge_University_Press.
- Krull_dimension wikiPageWikiLink Category:Commutative_algebra.
- Krull_dimension wikiPageWikiLink Category:Dimension.
- Krull_dimension wikiPageWikiLink Catenary_ring.
- Krull_dimension wikiPageWikiLink Codimension.
- Krull_dimension wikiPageWikiLink Cohen–Macaulay_ring.
- Krull_dimension wikiPageWikiLink Coherent_sheaf.
- Krull_dimension wikiPageWikiLink Coherent_sheaves.
- Krull_dimension wikiPageWikiLink Commutative_algebra.
- Krull_dimension wikiPageWikiLink Commutative_ring.
- Krull_dimension wikiPageWikiLink Convex_cone.
- Krull_dimension wikiPageWikiLink Dedekind_domain.
- Krull_dimension wikiPageWikiLink Depth_(ring_theory).
- Krull_dimension wikiPageWikiLink Deviation_of_a_poset.
- Krull_dimension wikiPageWikiLink Dimension_of_an_algebraic_variety.
- Krull_dimension wikiPageWikiLink Dimension_theory_(algebra).
- Krull_dimension wikiPageWikiLink Direct_product.
- Krull_dimension wikiPageWikiLink Discrete_valuation_ring.
- Krull_dimension wikiPageWikiLink Faithful_module.
- Krull_dimension wikiPageWikiLink Galois_connection.
- Krull_dimension wikiPageWikiLink Gelfand–Kirillov_dimension.
- Krull_dimension wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Krull_dimension wikiPageWikiLink Hilbert_function.
- Krull_dimension wikiPageWikiLink Hilbert_series_and_Hilbert_polynomial.
- Krull_dimension wikiPageWikiLink Homological_conjectures_in_commutative_algebra.
- Krull_dimension wikiPageWikiLink Integral_domain.
- Krull_dimension wikiPageWikiLink Integral_element.
- Krull_dimension wikiPageWikiLink Integral_extension.
- Krull_dimension wikiPageWikiLink Irving_Kaplansky.
- Krull_dimension wikiPageWikiLink Krulls_principal_ideal_theorem.
- Krull_dimension wikiPageWikiLink Local_ring.
- Krull_dimension wikiPageWikiLink Localization_of_a_ring.
- Krull_dimension wikiPageWikiLink Minimal_prime_ideal.
- Krull_dimension wikiPageWikiLink Module_(mathematics).
- Krull_dimension wikiPageWikiLink Noether_normalization_lemma.
- Krull_dimension wikiPageWikiLink Noetherian.
- Krull_dimension wikiPageWikiLink Noetherian_ring.
- Krull_dimension wikiPageWikiLink Normal_cone.
- Krull_dimension wikiPageWikiLink Polynomial_ring.
- Krull_dimension wikiPageWikiLink Prime_ideal.
- Krull_dimension wikiPageWikiLink Prime_ideals.
- Krull_dimension wikiPageWikiLink Principal_ideal_domain.
- Krull_dimension wikiPageWikiLink Reduced_ring.
- Krull_dimension wikiPageWikiLink Regular_local_ring.
- Krull_dimension wikiPageWikiLink Scheme_(mathematics).
- Krull_dimension wikiPageWikiLink Spectrum_of_a_ring.
- Krull_dimension wikiPageWikiLink Springer-Verlag.
- Krull_dimension wikiPageWikiLink Springer_Science+Business_Media.
- Krull_dimension wikiPageWikiLink Unique_factorization_domain.
- Krull_dimension wikiPageWikiLink Universally_catenary.
- Krull_dimension wikiPageWikiLink University_of_Chicago_Press.
- Krull_dimension wikiPageWikiLink Vector_bundle.
- Krull_dimension wikiPageWikiLink Vector_bundles.
- Krull_dimension wikiPageWikiLink Von_Neumann_regular_ring.
- Krull_dimension wikiPageWikiLink Wolfgang_Krull.
- Krull_dimension wikiPageWikiLink Zero_ring.
- Krull_dimension wikiPageWikiLinkText "2-dimensional".
- Krull_dimension wikiPageWikiLinkText "Krull dimension".
- Krull_dimension wikiPageWikiLinkText "dimension theory".
- Krull_dimension wikiPageWikiLinkText "dimension".
- Krull_dimension wikiPageWikiLinkText "dimensional".
- Krull_dimension wikiPageWikiLinkText "one-dimensional".
- Krull_dimension wikiPageWikiLinkText "zero-dimensional".
- Krull_dimension hasPhotoCollection Krull_dimension.
- Krull_dimension wikiPageUsesTemplate Template:Citation.
- Krull_dimension wikiPageUsesTemplate Template:Cite_book.
- Krull_dimension wikiPageUsesTemplate Template:Hartshorne_AG.
- Krull_dimension wikiPageUsesTemplate Template:Reflist.
- Krull_dimension subject Category:Commutative_algebra.
- Krull_dimension subject Category:Dimension.
- Krull_dimension hypernym Supremum.
- Krull_dimension comment "In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring.".
- Krull_dimension label "Krull dimension".
- Krull_dimension sameAs Krulldimension.
- Krull_dimension sameAs Dimensión_de_Krull.
- Krull_dimension sameAs Dimension_de_Krull.
- Krull_dimension sameAs ממד_קרול.
- Krull_dimension sameAs Dimensione_di_Krull.
- Krull_dimension sameAs クルル次元.
- Krull_dimension sameAs 크룰_차원.
- Krull_dimension sameAs Krull-dimensie.
- Krull_dimension sameAs m.0fjqz.
- Krull_dimension sameAs Размерность_Крулля.
- Krull_dimension sameAs Krullova_razsežnost.
- Krull_dimension sameAs Розмірність_Круля.
- Krull_dimension sameAs Q1225713.
- Krull_dimension sameAs Q1225713.
- Krull_dimension sameAs 克鲁尔维数.
- Krull_dimension wasDerivedFrom Krull_dimension?oldid=674573693.
- Krull_dimension isPrimaryTopicOf Krull_dimension.