Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:abbreviation |
PID
|
| gptkbp:defines |
An integral domain in which every ideal is principal
|
| gptkbp:example |
gptkb:The_ring_of_integers_Z
The ring of integers adjoined with sqrt(-5) The ring of polynomials over a field |
| gptkbp:field |
gptkb:Abstract_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Principal ideal domain
|
| gptkbp:namedFor |
gptkb:Richard_Dedekind
|
| gptkbp:property |
Every PID is a Noetherian domain
Every PID is a unique factorization domain Every nonzero prime ideal is maximal |
| gptkbp:relatedConcept |
gptkb:Unique_factorization_domain
gptkb:Ideal gptkb:Ring_theory Noetherian ring Euclidean domain |
| gptkbp:type |
gptkb:Integral_domain
|
| gptkbp:used_in |
gptkb:Commutative_algebra
gptkb:Algebraic_number_theory |
| gptkbp:bfsParent |
gptkb:Unique_Factorization_Domain
gptkb:Principal_ideal |
| gptkbp:bfsLayer |
7
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