Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:application |
homological algebra
module theory |
| gptkbp:category |
Artin algebra category is abelian
|
| gptkbp:defines |
An Artin algebra is a ring that is an algebra over an Artinian ring and is finitely generated as a module over that ring.
|
| gptkbp:hasProperty |
Krull-Schmidt property
every module decomposes into indecomposables finite number of simple modules |
| https://www.w3.org/2000/01/rdf-schema#label |
Artin algebras
|
| gptkbp:isA |
gptkb:associative_algebra
|
| gptkbp:namedAfter |
gptkb:Emil_Artin
|
| gptkbp:property |
finite-dimensional over a commutative Artinian ring
finite length as a module over its center |
| gptkbp:relatedTo |
gptkb:Artinian_ring
finite-dimensional algebra representation-finite algebra |
| gptkbp:studiedBy |
gptkb:Idun_Reiten
gptkb:Maurice_Auslander Jeremy Rickard |
| gptkbp:studiedIn |
gptkb:algebra
representation theory |
| gptkbp:bfsParent |
gptkb:Auslander–Reiten_theory
|
| gptkbp:bfsLayer |
7
|