Concept information
Terme préférentiel
algebraic number theory
Définition(s)
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Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory, like the existence of solutions to Diophantine equations.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Algebraic_number_theory)
Concept(s) générique(s)
Concept(s) spécifique(s)
- abelian variety
- adelic algebraic group
- algebraic number field
- Bring radical
- Brumer-Stark conjecture
- Chebotarev's density theorem
- class field theory
- congruence
- cyclotomic field
- elliptic curve
- Fermat's little theorem
- Galois module
- Minkowski's theorem
- modular arithmetic
- Newton polygon
- quadratic integer
- Roth's theorem
- Schwartz-Bruhat function
- solenoid
- Stark conjectures
- totally real number field
- valuation
Traductions
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français
URI
http://data.loterre.fr/ark:/67375/PSR-F7SFNL4R-1
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