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Flat module

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over a ring R is flat if 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…

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Overview

Definition

Relations to other module properties

Flat ring extensions

Local property

Faithful flatness

Homological characterization using Tor functors

Flat resolutions

Flat covers

In constructive mathematics

Advanced semantic analysis

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Map overview Semantic statistics

Flat module

Nodes97
Edges96
Triples44
Avg. degree1.98
Density0.020619
Components1

How this topic connects Entity context

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Flat module

Top relations

related to Flat covers · 12
Flat module → Bican, Eklof, El Bashir, Enochs, EnochsandJenda, Mac Lane, Since, The, This, Trlifaj, While, Xu
related to Examples · 7
Flat module → Every, For, If, Let, R-module, The, This
related to Non-examples · 6
Flat module → If, In, Noetherian, Over, R/I, Thus
related to Relations to other module properties · 5
Flat module → Flatness, However, In, Moreover, There
related to Torsion-free modules · 4
Flat module → Dedekind, Every, The, This
related to Direct sums, limits and products · 3
Flat module → Conversely, In, The
related to Flat resolutions · 3
Flat module → Any, Flat, Tor
related to In constructive mathematics · 3
Flat module → Flat, For, In

Important terminology Word statistics

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Important terminology

flat displaystyle module projective ring modules faithfully every free ideal finitely generated also flatness commutative mathfrak rings product direct torsion-free

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Mac Laneinstance ofand is covered in classics0.80text
Flat modulerelated to Direct sums, limits and productsThe0.60section
Flat modulerelated to Direct sums, limits and productsIn0.60section
Flat modulerelated to Direct sums, limits and productsConversely0.60section
Flat modulerelated to ExamplesR-module0.60section
Flat modulerelated to ExamplesFor0.60section
Flat modulerelated to ExamplesEvery0.60section
Flat modulerelated to ExamplesThis0.60section
Flat modulerelated to ExamplesIf0.60section
Flat modulerelated to ExamplesLet0.60section
Flat modulerelated to ExamplesThe0.60section
Flat modulerelated to Flat coversWhile0.60section

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    Min side: 3
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