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- 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 wikiPageRevisionID "597906118".
- Flat_module hasPhotoCollection Flat_module.
- Flat_module subject Category:Algebraic_geometry.
- Flat_module subject Category:Homological_algebra.
- Flat_module subject Category:Module_theory.
- Flat_module comment "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.".
- Flat_module label "Flachheit (Algebra)".
- Flat_module label "Flat module".
- Flat_module label "Module plat".
- Flat_module label "Modulo piatto".
- Flat_module label "Módulo plano".
- Flat_module label "Плоский модуль".
- Flat_module label "平坦模".
- Flat_module sameAs Flachheit_(Algebra).
- Flat_module sameAs Módulo_plano.
- Flat_module sameAs Module_plat.
- Flat_module sameAs Modulo_piatto.
- Flat_module sameAs 平坦加群.
- Flat_module sameAs m.02g_l2.
- Flat_module sameAs Q1426191.
- Flat_module sameAs Q1426191.
- Flat_module wasDerivedFrom Flat_module?oldid=597906118.
- Flat_module depiction FlatModule-01.png.
- Flat_module isPrimaryTopicOf Flat_module.
