Artinian modules

GPTKB entity

Statements (16)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:defines A module that satisfies the descending chain condition on submodules
gptkbp:field gptkb:algebra
https://www.w3.org/2000/01/rdf-schema#label Artinian modules
gptkbp:namedAfter gptkb:Emil_Artin
gptkbp:property A module over an Artinian ring is Artinian
Every descending chain of submodules terminates
Every simple module is Artinian
Every Artinian module is Noetherian if it is finitely generated over a commutative ring
gptkbp:relatedTo gptkb:Noetherian_modules
gptkb:Artinian_rings
gptkbp:usedIn representation theory
homological algebra
module theory
gptkbp:bfsParent gptkb:Noetherian_modules
gptkbp:bfsLayer 5