Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:contrastsWith |
gptkb:Noetherian_module
|
| gptkbp:defines |
A module that satisfies the descending chain condition on submodules
|
| gptkbp:example |
finite abelian group as a module over the integers
finite-dimensional vector space over a field |
| gptkbp:field |
gptkb:algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Artinian module
|
| gptkbp:namedAfter |
gptkb:Emil_Artin
|
| gptkbp:property |
Every descending chain of submodules terminates
Every simple module is Artinian Every Artinian module is Noetherian if it is of finite length |
| gptkbp:relatedTo |
gptkb:Noetherian_module
gptkb:Artinian_ring |
| gptkbp:usedIn |
representation theory
module theory ring theory |
| gptkbp:bfsParent |
gptkb:Noetherian_module
|
| gptkbp:bfsLayer |
5
|