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Flat Module: Abstract Algebra, Ring (mathematics), Module (mathematics) -

English
2026-03-06
€179.62 €224.53

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High Quality Content by WIKIPEDIA articles! In abstract algebra, 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 ... Full description

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High Quality Content by WIKIPEDIA articles! In abstract algebra, 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 local ring, flatness, projectivity, and freeness are all equivalent. In commutative algebra, and more generally in algebraic geometry, flatness has come to play a major role since Serre's paper Géometrie Algébrique et Géométrie Analytique. See also flat morphism.

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131198489
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€179.62 €224.53