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Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
integral domain |
| gptkbp:dimensions |
1
|
| gptkbp:every_nonzero_fractional_ideal_is |
invertible
|
| gptkbp:every_nonzero_proper_ideal_factors_uniquely_into |
product of prime ideals
|
| gptkbp:example |
polynomial ring in one variable over a field
ring of integers Z ring of integers of a number field |
| gptkbp:generalizes |
ring of integers in a number field
|
| gptkbp:hasProperty |
every nonzero ideal can be generated by at most two elements
every localization at a nonzero prime ideal is a discrete valuation ring |
| https://www.w3.org/2000/01/rdf-schema#label |
Dedekind domain
|
| gptkbp:isA |
Noetherian domain
commutative ring integrally closed domain |
| gptkbp:namedAfter |
gptkb:Richard_Dedekind
|
| gptkbp:not_necessarily |
principal ideal domain
unique factorization domain |
| gptkbp:used_in |
gptkb:algebraic_geometry
algebraic number theory |
| gptkbp:bfsParent |
gptkb:Richard_Dedekind
|
| gptkbp:bfsLayer |
4
|