Concept information
Preferred term
algebraic number theory
Definition(s)
-
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)
Broader concept(s)
Narrower concept(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
In other languages
URI
http://data.loterre.fr/ark:/67375/PSR-F7SFNL4R-1
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