Statements (36)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
Subset of a ring
|
| gptkbp:generalizes |
Normal subgroup (in group theory)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ideal
|
| gptkbp:introduced |
gptkb:Richard_Dedekind
|
| gptkbp:notation |
I, J, K (commonly used symbols)
|
| gptkbp:property |
Closed under addition
Every ring has at least two ideals: zero and unit ideal Absorbs multiplication by ring elements Finitely generated in Noetherian rings Generated by a subset Intersection of ideals is an ideal Maximal ideal is maximal under inclusion Prime ideal has special properties Principal ideal generated by a single element Product of ideals is an ideal Sum of ideals is an ideal Used in the definition of algebraic varieties Used to define factor rings |
| gptkbp:relatedTo |
gptkb:Maximal_ideal
gptkb:Prime_ideal gptkb:Principal_ideal gptkb:Quotient_ring Module Unit ideal Zero ideal |
| gptkbp:type |
gptkb:Left_ideal
gptkb:Two-sided_ideal Right ideal |
| gptkbp:usedIn |
gptkb:Number_theory
gptkb:Algebraic_geometry gptkb:Commutative_algebra gptkb:Ring_theory |
| gptkbp:bfsParent |
gptkb:Ben_Crompton
gptkb:Henry_Normal |
| gptkbp:bfsLayer |
5
|