Fitting ideal
E283606
The Fitting ideal is an algebraic invariant in commutative algebra and module theory that encodes information about the structure and relations of a finitely generated module over a ring.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Fitting ideal canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2636372 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fitting ideal Context triple: [Hans Fitting, notableConcept, Fitting ideal]
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A.
Fitter
Fitter is the NATO reporting name for the Soviet-designed Sukhoi Su-17/20/22 family of variable-sweep wing fighter-bomber aircraft.
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B.
Fittja
Fittja is a suburban district in the southern part of the Stockholm metropolitan area in Sweden, known for its diverse population and large-scale postwar housing.
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C.
Hilbert’s syzygy theorem
Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
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D.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
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E.
Hilbert’s Nullstellensatz
Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Fitting ideal Target entity description: The Fitting ideal is an algebraic invariant in commutative algebra and module theory that encodes information about the structure and relations of a finitely generated module over a ring.
-
A.
Fitter
Fitter is the NATO reporting name for the Soviet-designed Sukhoi Su-17/20/22 family of variable-sweep wing fighter-bomber aircraft.
-
B.
Fittja
Fittja is a suburban district in the southern part of the Stockholm metropolitan area in Sweden, known for its diverse population and large-scale postwar housing.
-
C.
Hilbert’s syzygy theorem
Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
-
D.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
E.
Hilbert’s Nullstellensatz
Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic invariant
ⓘ
ideal ⓘ notion in commutative algebra ⓘ notion in module theory ⓘ |
| 0thFittingIdealEncodes | annihilation information of a module ⓘ |
| alsoKnownAs | Fitting invariant ⓘ |
| associatedWith | finitely generated module ⓘ |
| constructedFrom | presentation matrix of a module ⓘ |
| constructedUsing | minors of a matrix ⓘ |
| definedOver | commutative ring ⓘ |
| dependsOn |
choice of module
ⓘ
ring structure ⓘ |
| encodes |
information about relations among generators of a module
ⓘ
information about the structure of a module ⓘ |
| hasGeneralization | Fitting invariant of a module ⓘ |
| hasIndexing | by nonnegative integers ⓘ |
| inAlgebraicGeometry |
controls scheme-theoretic support of coherent sheaves
ⓘ
defines closed subschemes ⓘ |
| inModuleDecomposition | helps distinguish nonisomorphic modules ⓘ |
| inNoetherianCase | finitely generated ideal ⓘ |
| inNumberTheory |
appears in Iwasawa theory
ⓘ
used to study class groups ⓘ |
| inRepresentationTheory | used for modules over group rings ⓘ |
| introducedBy | Hans Fitting ⓘ |
| isFunctorial | yes ⓘ |
| isMonotoneInIndex | yes ⓘ |
| notation | Fitt_R^i(M) ⓘ |
| relatedTo |
annihilator of a module
ⓘ
determinantal ideals ⓘ rank of a module ⓘ support of a module ⓘ |
| specialCase | 0th Fitting ideal ⓘ |
| stableUnder | base change in many situations ⓘ |
| usedIn |
algebraic geometry
ⓘ
classification of modules ⓘ commutative algebra ⓘ deformation theory ⓘ determinantal varieties ⓘ singularity theory ⓘ study of module presentations ⓘ |
| usedToControl | where a module is locally free ⓘ |
| usedToDefine | Fitting support of a module ⓘ |
| usedToDescribe | degeneracy loci of maps of vector bundles ⓘ |
| usedToDetect |
projective dimension in some cases
ⓘ
torsion in modules ⓘ |
| yearIntroduced | 1936 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Fitting ideal Description of subject: The Fitting ideal is an algebraic invariant in commutative algebra and module theory that encodes information about the structure and relations of a finitely generated module over a ring.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.