Arf closure
E654174
Arf closure is a concept in commutative algebra introduced by mathematician Cahit Arf that refines integral closure to better control singularities in one-dimensional local rings and semigroups.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Arf closure canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7281891 — 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: Arf closure Context triple: [Cahit Arf, knownFor, Arf closure]
-
A.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
-
B.
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.
-
C.
Knuth–Bendix completion algorithm
The Knuth–Bendix completion algorithm is a procedure in term rewriting and automated theorem proving that transforms a set of equations into a confluent rewriting system, enabling decision of word problems in algebraic structures.
-
D.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
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E.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
- 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: Arf closure Target entity description: Arf closure is a concept in commutative algebra introduced by mathematician Cahit Arf that refines integral closure to better control singularities in one-dimensional local rings and semigroups.
-
A.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
-
B.
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.
-
C.
Knuth–Bendix completion algorithm
The Knuth–Bendix completion algorithm is a procedure in term rewriting and automated theorem proving that transforms a set of equations into a confluent rewriting system, enabling decision of word problems in algebraic structures.
-
D.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
E.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
- F. None of above. chosen
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
closure operation
ⓘ
concept in commutative algebra ⓘ |
| appliesTo |
one-dimensional local rings
ⓘ
semigroups ⓘ |
| characteristicProperty | stability under blowing up in dimension one ⓘ |
| context |
curve singularities
ⓘ
one-dimensional analytically irreducible local domains ⓘ |
| ensures | certain regularity conditions on value semigroups ⓘ |
| field | commutative algebra ⓘ |
| generalizes | Arf rings ⓘ |
| goal | to obtain better-behaved singularities than with integral closure alone ⓘ |
| introducedBy | Cahit Arf NERFINISHED ⓘ |
| namedAfter | Cahit Arf NERFINISHED ⓘ |
| purpose | to better control singularities ⓘ |
| refines | integral closure ⓘ |
| relatedTo |
Arf ring
ⓘ
integral closure of ideals ⓘ value semigroup of a curve singularity ⓘ |
| studiedIn |
singularity theory of algebraic curves
ⓘ
theory of numerical semigroups ⓘ |
| typeOf |
closure operation on rings
ⓘ
closure operation on semigroups ⓘ |
| usedFor | resolution of singularities in dimension one ⓘ |
| usedIn |
study of numerical semigroups
ⓘ
study of one-dimensional local rings ⓘ |
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: Arf closure Description of subject: Arf closure is a concept in commutative algebra introduced by mathematician Cahit Arf that refines integral closure to better control singularities in one-dimensional local rings and semigroups.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.