Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Flat_module> ?p ?o }
- Flat_module abstract "In homological algebra and algebraic geometry, a flat module over a ring R is an R-module M such that taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact.Vector spaces over a field are flat modules. Free modules, or more generally projective modules, are also flat, over any R. For finitely generated modules over a Noetherian ring, flatness and projectivity are equivalent. For finitely generated modules over local rings, flatness, projectivity and freeness are all equivalent. The field of quotients of an integral domain, and, more generally, any localization of a commutative ring are flat modules. The product of the local rings of a commutative ring is a faithfully flat module.Flatness was introduced by Serre (1956) in his paper Géometrie Algébrique et Géométrie Analytique. See also flat morphism.".
- Flat_module thumbnail FlatModule-01.png?width=300.
- Flat_module wikiPageExternalLink item?id=AIF_1956__6__1_0.
- Flat_module wikiPageID "492616".
- Flat_module wikiPageLength "17013".
- Flat_module wikiPageOutDegree "87".
- Flat_module wikiPageRevisionID "661798847".
- Flat_module wikiPageWikiLink Abelian_group.
- Flat_module wikiPageWikiLink Academic_Press.
- Flat_module wikiPageWikiLink Algebraic_geometry.
- Flat_module wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Flat_module wikiPageWikiLink Annales_de_lInstitut_Fourier.
- Flat_module wikiPageWikiLink Artinian_local_ring.
- Flat_module wikiPageWikiLink Artinian_ring.
- Flat_module wikiPageWikiLink Axiom_of_choice.
- Flat_module wikiPageWikiLink Cambridge_University_Press.
- Flat_module wikiPageWikiLink Category:Algebraic_geometry.
- Flat_module wikiPageWikiLink Category:Homological_algebra.
- Flat_module wikiPageWikiLink Category:Module_theory.
- Flat_module wikiPageWikiLink Cohen–Macaulay_ring.
- Flat_module wikiPageWikiLink Coherent_ring.
- Flat_module wikiPageWikiLink Colimits.
- Flat_module wikiPageWikiLink Commutative_ring.
- Flat_module wikiPageWikiLink Completion_(algebra).
- Flat_module wikiPageWikiLink Completion_(ring_theory).
- Flat_module wikiPageWikiLink Constructive_mathematics.
- Flat_module wikiPageWikiLink Constructivism_(mathematics).
- Flat_module wikiPageWikiLink Daniel_Lazard.
- Flat_module wikiPageWikiLink Dedekind_domain.
- Flat_module wikiPageWikiLink Dedekind_ring.
- Flat_module wikiPageWikiLink Derived_functor.
- Flat_module wikiPageWikiLink Direct_limit.
- Flat_module wikiPageWikiLink Direct_sum_of_modules.
- Flat_module wikiPageWikiLink Epimorphism.
- Flat_module wikiPageWikiLink Essential_extension.
- Flat_module wikiPageWikiLink Exact_functor.
- Flat_module wikiPageWikiLink Exact_sequence.
- Flat_module wikiPageWikiLink Factor_module.
- Flat_module wikiPageWikiLink Field_(mathematics).
- Flat_module wikiPageWikiLink Field_of_fractions.
- Flat_module wikiPageWikiLink Field_of_quotients.
- Flat_module wikiPageWikiLink Finitely-generated_module.
- Flat_module wikiPageWikiLink Finitely-presented_module.
- Flat_module wikiPageWikiLink Finitely_generated_module.
- Flat_module wikiPageWikiLink Flat_dimension.
- Flat_module wikiPageWikiLink Flat_morphism.
- Flat_module wikiPageWikiLink Free_module.
- Flat_module wikiPageWikiLink Frobenius_endomorphism.
- Flat_module wikiPageWikiLink Frobenius_morphism.
- Flat_module wikiPageWikiLink Generic_flatness.
- Flat_module wikiPageWikiLink Géometrie_Algébrique_et_Géométrie_Analytique.
- Flat_module wikiPageWikiLink Homological_algebra.
- Flat_module wikiPageWikiLink Injective.
- Flat_module wikiPageWikiLink Injective_function.
- Flat_module wikiPageWikiLink Integral_domain.
- Flat_module wikiPageWikiLink Limit_(category_theory).
- Flat_module wikiPageWikiLink Local_ring.
- Flat_module wikiPageWikiLink Localization_of_a_module.
- Flat_module wikiPageWikiLink Localization_of_a_ring.
- Flat_module wikiPageWikiLink Long_exact_sequence.
- Flat_module wikiPageWikiLink Maximal_ideal.
- Flat_module wikiPageWikiLink Module_(mathematics).
- Flat_module wikiPageWikiLink Module_homomorphism.
- Flat_module wikiPageWikiLink Noetherian_ring.
- Flat_module wikiPageWikiLink Perfect_ring.
- Flat_module wikiPageWikiLink Prime_ideal.
- Flat_module wikiPageWikiLink Projective_cover.
- Flat_module wikiPageWikiLink Projective_module.
- Flat_module wikiPageWikiLink Prüfer_domain.
- Flat_module wikiPageWikiLink Pure_submodule.
- Flat_module wikiPageWikiLink Quotient_module.
- Flat_module wikiPageWikiLink Regular_local_ring.
- Flat_module wikiPageWikiLink Regular_ring.
- Flat_module wikiPageWikiLink Resolution_(algebra).
- Flat_module wikiPageWikiLink Resolution_of_a_module.
- Flat_module wikiPageWikiLink Right_exact_functor.
- Flat_module wikiPageWikiLink Ring_(mathematics).
- Flat_module wikiPageWikiLink Short_exact_sequence.
- Flat_module wikiPageWikiLink Springer-Verlag.
- Flat_module wikiPageWikiLink Springer_Science+Business_Media.
- Flat_module wikiPageWikiLink Submodule.
- Flat_module wikiPageWikiLink Superfluous_submodule.
- Flat_module wikiPageWikiLink Tensor_product.
- Flat_module wikiPageWikiLink Tor_functor.
- Flat_module wikiPageWikiLink Torsion-free_module.
- Flat_module wikiPageWikiLink Torsion_(algebra).
- Flat_module wikiPageWikiLink Torsion_element.
- Flat_module wikiPageWikiLink Vector_space.
- Flat_module wikiPageWikiLink Von_Neumann_regular_ring.
- Flat_module wikiPageWikiLink Weak_dimension.
- Flat_module wikiPageWikiLink Zariski_ring.
- Flat_module wikiPageWikiLink File:FlatModule-01.png.
- Flat_module wikiPageWikiLink File:Module_properties_in_commutative_algebra.svg.
- Flat_module wikiPageWikiLink File:Short_exact_sequence_ABC.png.
- Flat_module wikiPageWikiLinkText "Flat module".
- Flat_module wikiPageWikiLinkText "characterization of flatness".
- Flat_module wikiPageWikiLinkText "flat module".
- Flat_module wikiPageWikiLinkText "flat module#Categorical colimits".
- Flat_module wikiPageWikiLinkText "flat module#Flat resolutions".
- Flat_module wikiPageWikiLinkText "flat right modules".