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Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:characterizedBy |
Ascending chain condition on submodules
|
| gptkbp:defines |
A module in which every submodule is finitely generated
A module in which every ascending chain of submodules stabilizes |
| gptkbp:example |
Any finite module
Finitely generated modules over a Noetherian ring The zero module |
| gptkbp:field |
gptkb:algebra
|
| gptkbp:generalizes |
gptkb:Noetherian_rings
|
| https://www.w3.org/2000/01/rdf-schema#label |
Noetherian modules
|
| gptkbp:implies |
Every submodule is finitely generated
|
| gptkbp:namedAfter |
gptkb:Emmy_Noether
|
| gptkbp:opposedBy |
gptkb:Artinian_modules
|
| gptkbp:property |
Every submodule of a Noetherian module is Noetherian
Finite direct sums of Noetherian modules are Noetherian Quotients of Noetherian modules are Noetherian Submodules of Noetherian modules are Noetherian |
| gptkbp:relatedTo |
gptkb:Noetherian_rings
|
| gptkbp:usedIn |
gptkb:commutative_algebra
homological algebra module theory |
| gptkbp:bfsParent |
gptkb:Emmy_Noether
|
| gptkbp:bfsLayer |
4
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