Theorie der algebraischen Zahlen
E483406
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Theorie der algebraischen Zahlen canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T4962221 — 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: Theorie der algebraischen Zahlen Context triple: [Kurt Hensel, publication, Theorie der algebraischen Zahlen]
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A.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
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B.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
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C.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
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D.
Theorie der algebraischen Kurven
"Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
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E.
Neukirch: Algebraic Number Theory
"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
- 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: Theorie der algebraischen Zahlen Target entity description: "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
-
A.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
B.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
C.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
D.
Theorie der algebraischen Kurven
"Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
-
E.
Neukirch: Algebraic Number Theory
"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic number theory monograph
ⓘ
mathematics book ⓘ |
| associatedWith |
Hensel lifting
ⓘ
linked to:
Hensel’s lemma
Henselian fields ⓘ p-adic analysis ⓘ |
| author | Kurt Hensel ⓘ |
| contributedTo | foundations of algebraic number theory ⓘ |
| countryOfOrigin | Germany ⓘ |
| field | algebraic number theory ⓘ |
| hasAuthorRole | Kurt Hensel as originator of p-adic numbers ⓘ |
| hasKeyConcept |
algebraic integers
ⓘ
completion of number fields ⓘ ideals in number fields ⓘ local–global methods in number theory ⓘ p-adic numbers ⓘ p-adic valuation ⓘ prime decomposition in number fields ⓘ |
| historicalPeriod | early 20th century mathematics ⓘ |
| influenced |
local field theory
ⓘ
modern number theory ⓘ valuation theory ⓘ |
| language | German ⓘ |
| namedAfter | algebraic numbers ⓘ |
| notableFor |
development of p-adic number theory
ⓘ
introduction of p-adic numbers ⓘ |
| topic |
arithmetic of algebraic numbers
ⓘ
congruences and valuations ⓘ extensions of the rational numbers ⓘ factorization in number fields ⓘ structure of algebraic number fields ⓘ |
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: Theorie der algebraischen Zahlen Description of subject: "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Hensel