Cassels–Fröhlich: Algebraic Number Theory
E462233
Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Cassels–Fröhlich: Algebraic Number Theory canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T4597226 — 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: Cassels–Fröhlich: Algebraic Number Theory Context triple: [Kronecker–Weber theorem, standardReference, Cassels–Fröhlich: Algebraic Number Theory]
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A.
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.
-
B.
A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
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.
-
E.
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.
- 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: Cassels–Fröhlich: Algebraic Number Theory Target entity description: Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
-
A.
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.
-
B.
A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic number theory book
ⓘ
mathematics book ⓘ textbook ⓘ |
| discipline |
algebra
ⓘ
number theory ⓘ |
| editor |
A. Fröhlich
ⓘ
linked to:
Herbert Fröhlich
J. W. S. Cassels ⓘ |
| field | algebraic number theory ⓘ |
| hasContributor |
A. Fröhlich
ⓘ
linked to:
Herbert Fröhlich
J. W. S. Cassels ⓘ |
| intendedAudience |
graduate students
ⓘ
research mathematicians ⓘ |
| isClassicIn | algebraic number theory ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| publicationType | edited volume ⓘ |
| publisher | Academic Press ⓘ |
| title |
Algebraic Number Theory
ⓘ
linked to:
algebraic number theory
|
| topic |
Brauer groups
ⓘ
Chebotarev density theorem ⓘ Dedekind domains ⓘ Dirichlet unit theorem ⓘ Galois cohomology ⓘ Galois theory of number fields ⓘ Hasse principle ⓘ Kronecker–Weber theorem ⓘ L-functions ⓘ Minkowski theory ⓘ
linked to:
Minkowski’s theorem on convex sets
algebraic number fields ⓘ class field theory ⓘ class groups ⓘ cohomological methods in number theory ⓘ cyclotomic fields ⓘ discriminants of number fields ⓘ global class field theory ⓘ global fields ⓘ ideals in number fields ⓘ ideles and adeles ⓘ local class field theory ⓘ local fields ⓘ local-global principles ⓘ norms and traces in number fields ⓘ prime decomposition in extensions ⓘ ramification theory ⓘ units in number fields ⓘ valuations ⓘ zeta functions of number fields ⓘ |
| usedAs | standard reference in algebraic number theory courses ⓘ |
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: Cassels–Fröhlich: Algebraic Number Theory Description of subject: Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.