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See Also: norm and trace of algebraic number, modular form, Hecke operator, bibliography for number theory, the arithmetic of elliptic curves, topics on ideal class groups and discriminants, examples of ring of integers of a number field, number field, theory of algebraic and transcendental numbers, theory of rational and irrational numbers, norm and trace of algebraic number, Hecke algebra, basis of ideal in algebraic number field, table of some fundamental units
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Cross-references: Hecke operators, Hecke algebra, modular form, the arithmetic of elliptic curves, Galois representations, order, absolute Galois group, number, infinite Galois theory, infinite, examples for Hensel's lemma, roots, Hensel's lemma, discrete valuation rings, valuation, completion, local fields, prime, ray class groups, ray class fields, isomorphic, Galois group, key, Hilbert class field, Artin map, complex multiplication, elliptic curves, abelian extensions of quadratic imaginary number fields, Kronecker-Weber theorem, abelian extensions, theory, class, class number formula, Dedekind zeta function, Riemann hypothesis, zeta function, the cyclotomic units are algebraic units, cyclotomic field, subgroup, cyclotomic units, invariant, regulator, units of quadratic fields, fundamental units, Dirichlet's unit theorem, structure, unit group, topics on ideal class groups and discriminants, class number, arithmetic, quotient group, ideal class group, calculating the splitting of primes, examples of prime ideal decomposition in number fields, ramification of archimedean places, decomposition group, inertia group, definitions, splitting and ramification in number fields and Galois extensions, extension, ideals, prime ideals, product, factors, example of ring which is not a UFD, UFD, NOR, PID, multiplication ring, Prüfer ring, multiplication, group, invertible, fractional ideal, Dedekind domain, Euclidean, field, ramification, measures, discriminant, norm of an ideal, trace, norm, totally real and imaginary fields, real and complex embeddings, examples of ring of integers of a number field, commutative ring, algebraic integers, ring of integers, algebraic, a finite extension of fields is an algebraic extension, finite field extension, number field, object, theory of algebraic and transcendental numbers, complementary, theory of rational and irrational numbers, applications, properties, algebraic numbers, Fermat's last theorem, Pythagorean triples, equations, polynomial, solutions, integer, contains, number theory, reference, sections, expanded, PlanetMath
There are 12 references to this entry.
This is version 31 of algebraic number theory, born on 2005-03-15, modified 2007-04-08.
Object id is 6878, canonical name is AlgebraicNumberTheory.
Accessed 13864 times total.
Classification:
| AMS MSC: | 11-01 (Number theory :: Instructional exposition ) | | | 11R99 (Number theory :: Algebraic number theory: global fields :: Miscellaneous) | | | 11S99 (Number theory :: Algebraic number theory: local and $p$-adic fields :: Miscellaneous) |
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Pending Errata and Addenda
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