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- Global_dimension abstract "In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A, is a non-negative integer or infinity which is a homological invariant of the ring. It is defined to be the supremum of the set of projective dimensions of all A-modules. Global dimension is an important technical notion in the dimension theory of Noetherian rings. By a theorem of Jean-Pierre Serre, global dimension can be used to characterize within the class of commutative Noetherian local rings those rings which are regular. Their global dimension coincides with the Krull dimension, whose definition is module-theoretic.When the ring A is noncommutative, one initially has to consider two versions of this notion, right global dimension that arises from consideration of the right A-modules, and left global dimension that arises from consideration of the left A-modules. For an arbitrary ring A the right and left global dimensions may differ. However, if A is a Noetherian ring, both of these dimensions turn out to be equal to weak global dimension, whose definition is left-right symmetric. Therefore, for noncommutative Noetherian rings, these two versions coincide and one is justified in talking about the global dimension.".
- Global_dimension wikiPageID "2291739".
- Global_dimension wikiPageLength "5328".
- Global_dimension wikiPageOutDegree "40".
- Global_dimension wikiPageRevisionID "702615239".
- Global_dimension wikiPageWikiLink Category:Dimension.
- Global_dimension wikiPageWikiLink Category:Homological_algebra.
- Global_dimension wikiPageWikiLink Category:Module_theory.
- Global_dimension wikiPageWikiLink Category:Ring_theory.
- Global_dimension wikiPageWikiLink Commutative_ring.
- Global_dimension wikiPageWikiLink Cyclic_module.
- Global_dimension wikiPageWikiLink David_Hilbert.
- Global_dimension wikiPageWikiLink Domain_(ring_theory).
- Global_dimension wikiPageWikiLink Field_(mathematics).
- Global_dimension wikiPageWikiLink Finitely_generated_module.
- Global_dimension wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Global_dimension wikiPageWikiLink Hereditary_ring.
- Global_dimension wikiPageWikiLink Hilberts_syzygy_theorem.
- Global_dimension wikiPageWikiLink Homological_algebra.
- Global_dimension wikiPageWikiLink Infimum_and_supremum.
- Global_dimension wikiPageWikiLink Injective_module.
- Global_dimension wikiPageWikiLink Jean-Pierre_Serre.
- Global_dimension wikiPageWikiLink Krull_dimension.
- Global_dimension wikiPageWikiLink Local_ring.
- Global_dimension wikiPageWikiLink Maximal_ideal.
- Global_dimension wikiPageWikiLink Module_(mathematics).
- Global_dimension wikiPageWikiLink Noetherian_ring.
- Global_dimension wikiPageWikiLink Polynomial_ring.
- Global_dimension wikiPageWikiLink Principal_ideal_domain.
- Global_dimension wikiPageWikiLink Projective_module.
- Global_dimension wikiPageWikiLink Regular_local_ring.
- Global_dimension wikiPageWikiLink Residue_field.
- Global_dimension wikiPageWikiLink Ring_(mathematics).
- Global_dimension wikiPageWikiLink Ring_theory.
- Global_dimension wikiPageWikiLink Semisimple_module.
- Global_dimension wikiPageWikiLink Triangular_matrix_ring.
- Global_dimension wikiPageWikiLink Weak_dimension.
- Global_dimension wikiPageWikiLink Weyl_algebra.
- Global_dimension wikiPageWikiLinkText "Global dimension".
- Global_dimension wikiPageWikiLinkText "global dimension".
- Global_dimension wikiPageUsesTemplate Template:Citation.
- Global_dimension subject Category:Dimension.
- Global_dimension subject Category:Homological_algebra.
- Global_dimension subject Category:Module_theory.
- Global_dimension subject Category:Ring_theory.
- Global_dimension hypernym Integer.
- Global_dimension comment "In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A, is a non-negative integer or infinity which is a homological invariant of the ring. It is defined to be the supremum of the set of projective dimensions of all A-modules. Global dimension is an important technical notion in the dimension theory of Noetherian rings.".
- Global_dimension label "Global dimension".
- Global_dimension sameAs Q5570832.
- Global_dimension sameAs Dimension_homologique.
- Global_dimension sameAs 大局次元.
- Global_dimension sameAs 호몰로지_차원.
- Global_dimension sameAs m.071byk.
- Global_dimension sameAs Q5570832.
- Global_dimension sameAs 內射維度、投射維度與同調維度.
- Global_dimension wasDerivedFrom Global_dimension?oldid=702615239.
- Global_dimension isPrimaryTopicOf Global_dimension.