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