Ash R.B. — A Course In Algebraic Number Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Ash R.B. — A Course In Algebraic Number Theory

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Название: A Course In Algebraic Number Theory

Автор: Ash R.B.

Аннотация:

This is a text for a basic course in algebraic number theory.

Язык:

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 95

Добавлена в каталог: 28.11.2004

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Предметный указатель

Absolute value      9-1
Absolute value on the rationals      9-4
AKLB setup      2-5
Algebraic integer      1-2
Approximation theorem      9-5 9-6
Archimedean absolute value      9-1
Artin symbol      8-5
Artin-Whaples      see “Approximation theorem”
Cauchy sequence      9-7
Characteristic polynomial      2-1
Class number      5-7
Coherent sequence      9-8
Completion of a field with an absolute value      9-7
Conjugates of an element      2-3
Conjugates of an element, of a prime ideal      8-2
Contraction of an ideal      4-1
Cyclotomic extension      2-5 2-7 6-5 7-1 8-6
Cyclotomic extension, polynomial      7-1
Decomposition field      8-6
Decomposition group      8-2
Dedekind domain      3-1
Dedekind’s lemma      2-4
Denominator of a fractional ideal      3-3
Dirichlet unit theorem      6-1 6-3 6-4
Discrete valuation      9-1
Discrete valuation ring      4-3 9-2 9-3
Discriminant      2-8 7-3 7-4
Divides means contains      3-6
DVR      see “Discrete valuation ring”
Embedding, canonical      5-4
Embedding, complex      5-4
Embedding, logarithmic      6-1
Embedding, real      5-4
Equation of integral dependence      1-2
Equivalent absolute values      9-4
Extension of an ideal      4-1
Factoring of prime ideals in extensions      4-1
Field discriminant      2-10
Fractional ideal      3-2 3-3
Frobenius automorphism      8-4
Fundamental domain      5-1
Fundamental system of units      6-5
Fundamental unit      6-6
Galois extensions      8-1ff
Global field      9-1
Greatest common divisor of ideals      3-6
Hensel’s Lemma      9-10
Ideal class group      3-8
Ideal class group, finiteness of      5-6
Inert prime      4-8
Inertia field      8-6
Inertia group      8-2
Inertial degree      see “Relative degree”
Infinite prime      9-5
Integral basis      2-10 2-11
Integral basis of a cyclotomic field      7-4ff
Integral closure      1-3
Integral element, extension      1-2ff
Integral ideal      3-3
Integrally closed      1-3
Isosceles triangle      9-3

Kummer’s Theorem      4-7
Lattice      5-1
Least common multiple of ideals      3-6
Lifting of prime ideals      4-1
Local field      9-1 9-8
Local ring      1-7
localization      1-5ff
Localization of modules      1-7
Localization, functor      1-8
Localized ring      1-5
Lying over      4-1
Minimal polynomial      2-2
Minkowski bound on element norms      5-5
Minkowski bound on ideal norms      5-6
Minkowski’s convex body theorem      5-2
Multiplicative property of norms      2-2 4-4 4-5
Multiplicative set      1-5
Nonarchimedean absolute value      9-1
Nondegenerate bilinear form      2-4
Norm      1-1 2-1
Norm of an ideal      4-4
Null sequence      9-7
Number field      2-5
Number ring      4-4
P-adic (and p-adic) valuation      9-2
p-adic integers      9-9
p-adic logarithm and exponential      9-9
p-adic numbers      9-9
Power series      9-8
Prime avoidance lemma      3-2
Prime element      9-8
Principal fractional ideal      3-8
Product formula      9-5
Quadratic extension      2-4 2-6 2-7 4-8 6-6 6-7
Quadratic reciprocity      8-8
Ram-rel identity      4-2
Ramification      4-2
Ramification and the discriminant      4-6
Ramification of a prime      4-8
Ramification, index      4-2
ransitivity of trace and norm      2-4
Rational integers      2-6 2-11
Relative degree      4-2
Residue class degree      see “Relative degree”
Residue field      9-10
Ring of fractions      1-5
Splitting of a prime      4-8
Stabilizing a module      1-2
Stickelberger’s theorem      2-12
Totally ramified      8-8
Trace      2-1
Trace, form      2-4
Transitivity of integral extensions      1-3
Trivial absolute value      9-2
Uniformizer      9-8
Unimodular matrix      2-11 5-1
Unique factorization of ideals      3-5
Unit theore      see “Dirichlet unit theorem”
Valuation ideal      9-2
Valuation ring      9-2
Vandermonde determinant      2-9

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