Die Theorie der algebraischen Zahlkörper
E208854
"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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Die Theorie der algebraischen Zahlkörper canonical | 2 |
| Hilberts Zahlbericht | 2 |
| Hilbert’s Zahlbericht | 1 |
| Hilbert’s report on algebraic number theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1859313 — 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.
Target entity: Die Theorie der algebraischen Zahlkörper Context triple: [Zahlbericht, title, Die Theorie der algebraischen Zahlkörper]
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A.
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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B.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
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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.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
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E.
Moderne Algebra
Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Die Theorie der algebraischen Zahlkörper Target entity description: "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.
-
A.
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.
-
B.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
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.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
E.
Moderne Algebra
Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ treatise ⓘ |
| aimsAt | systematic exposition of algebraic number fields ⓘ |
| author | David Hilbert ⓘ |
| citedAs |
Die Theorie der algebraischen Zahlkörper
self-linksurface differs
ⓘ
surface form:
Hilberts Zahlbericht
|
| countryOfPublication | German Empire ⓘ |
| describes |
algebraic number fields
ⓘ
class groups ⓘ decomposition of prime ideals ⓘ discriminants of number fields ⓘ ideals in number fields ⓘ norms and traces in number fields ⓘ ramification in extensions of number fields ⓘ units in number fields ⓘ zeta functions of number fields ⓘ |
| field | algebraic number theory ⓘ |
| hasAlternativeName |
Die Theorie der algebraischen Zahlkörper
ⓘ
surface form:
Hilberts Zahlbericht
|
| hasAuthor | David Hilbert ⓘ |
| hasInfluenceOn |
class field theory
ⓘ
ideal theory ⓘ modern algebraic number theory ⓘ |
| historicalRole | synthesized 19th-century work in algebraic number theory ⓘ |
| impact | standard reference for early 20th-century number theorists ⓘ |
| influenced |
Emil Artin
ⓘ
Helmut Hasse ⓘ class field theory textbooks ⓘ |
| isFoundationalWorkIn | algebraic number theory ⓘ |
| language | German ⓘ |
| mainTopic | algebraic number fields ⓘ |
| mathematicalDiscipline |
algebra
ⓘ
number theory ⓘ |
| originalTitle | Die Theorie der algebraischen Zahlkörper self-link ⓘ |
| partOf | Zahlbericht ⓘ |
| publicationCentury | 20th century ⓘ |
| publisher | Jahresbericht der Deutschen Mathematiker-Vereinigung ⓘ |
| subjectOf | historical studies in mathematics ⓘ |
| titleLanguage | de ⓘ |
| usesConcept |
Galois extension
ⓘ
class number ⓘ discriminant ⓘ field extension ⓘ ideal ⓘ prime ideal ⓘ ring of integers of a number field ⓘ unit group ⓘ |
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Subject: Die Theorie der algebraischen Zahlkörper Description of subject: "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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.