structure theorem for modules over a PID
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
fundamental theorem of finitely generated modules over a PID
|
| gptkbp:appliesTo |
finitely generated modules
principal ideal domains |
| gptkbp:field |
gptkb:algebra
module theory |
| https://www.w3.org/2000/01/rdf-schema#label |
structure theorem for modules over a PID
|
| gptkbp:implies |
gptkb:Jordan_canonical_form
rational canonical form classification of finitely generated abelian groups |
| gptkbp:provenBy |
gptkb:Emmy_Noether
others in early 20th century |
| gptkbp:publishedIn |
various algebra textbooks
|
| gptkbp:relatedTo |
gptkb:Smith_normal_form
elementary divisors invariant factor decomposition |
| gptkbp:state |
Every finitely generated module over a principal ideal domain is a direct sum of a free module and a finite number of cyclic modules.
|
| gptkbp:usedIn |
gptkb:topology
representation theory linear algebra homological algebra |
| gptkbp:bfsParent |
gptkb:Ring_theory
|
| gptkbp:bfsLayer |
7
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