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| Cohn P.M. — Algebraic Numbers and Algebraic Functions |
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| Предметный указатель |
Abel — Jacobi theorem 155 172
Abel’s theorem 163
Absolute norm, unit 10
Absolute residue degree 110
Absolute value 1
Addition theorem 157 162
Adele 126
Algebraic function field 109
Algebraic integer 84
Algebraic number 83ff
Analytic isomorphism 7
Anharmonic case (elliptic function field) 165
Approximation theorem 8
Archimedean 3
Archimedean ordering 33
Archimedes 287—212
Artin, E. 10 15 83
Associated elements 21
atom 71
based 114
Bloch, A. 163
Branchpoint 111
Canonical divisor class 139
Cantor, G. 83
Casorati — Weierstrass theorem 163
Cauchy sequence 12
Cauchy’s Theorem 140 168
Chain rule 136
Chevalley, C. 47 105
Chinese remainder theorem 8
Class number 106
Complement 72
Complete, completion 12
Completion by cuts 32
Composite of fields 55
Conorm map 70
Constants (field of) 98
Convergent 11
Convex subgroup 31
Coprime 115
Critical order 139
Cubical norm 14
Decomposed prime 88
Dedekind cut 32
Dedekind discriminant theorem 79
Dedekind domain 64
Dedekind, J.W.R. 32 91
Deficiency 129
Degree 85 110 115 123
Denominator 115 118
Derivation 135
Different 74
Differential 137
Differential, first kind 145
Differential, second, third kind 162
Direct product 55
Dirichlet, P.G.L. 105
Discrete ordered group 34
Discrete subgroup of R 103
Discrete valuation 19
Discriminant 76
divides 67 115
Divisor (group) 61 114
Divisor class group 69
Divisor of poles, zeros 118
Domination 20
Dual basis 73
Einseinheit 26
Elliptic function field 130
Elliptic integral 160
Elliptic modular function 164
Equivalent absolute values 7
Equivalent valuations 21
Euclidean algorithm 89
Fermat’s Last Theorem 134
Field composite 55
Field of constants 98
Fractional ideal 61
Function field 109
Fundamental domain 161
Gap 148
Gauss, C.F. 177—185
Gaussian extension 47
Gaussian integer 84
Gauss’s Lemma 85
Gelfand — Mazur theorem 16
Gelfand, I.M. 191
General valuation 19
Genus 125 129 146ff
Global field 95 97
Golod, E.S. 108
Group algebra 41
Haar integral 26
Hausdorff separation axiom 10
Hensel’s Lemma 47 51
Hilbert’s theory of ramification 81
Hyperelliptic field 149
Ideal class group 106
Inert prime 88
Inertia subgroup 54
Integral at p 59
Integral closure, element 48
Integral divisor 115
Integral ideal 61
Invertible ideal 61
Irreducible element 71
Isolated divisor 124
Isomorphic places 24
Jacobian variety 123 171
Jacobi’s theorem 174
Koebe, P. 168
Krull valuation 19
Krull, W. 18
Lagrange interpolation formula 75
Laurent series 30
Lemniscate 165
| Lexicographic ordering 34ff
Liiroth’s theorem 148
Lindemann, C.L.F. 84
Linear series 124 128 158
Liouville, J. 84
Liouville’s theorem 114
Local field 99
Local ring 38
localization 38
Lower segment 32
Majorize 32
Manifold 131
Mazur, S. 16
Metric space 6
Minkowski constant 108
Minkowski, H. 105
Minkowski’s theorem 100
Mittag — Leffler’s theorem 112
Multiplicative group of a field 89
Noether, E. 58 64ff
Noether, M. 150
Noetherian ring 64
Noether’s theorem 148
Non-archimedean 3
Norm 5 76
Norm map 70
Normalized valuation 19
Normed vector space 13
Numerator 115 118
Order 3
Order of a parallelotope 95
Order-homomorphism 31
Ordered field 42
Ordered group 31
Ostrowski, A. 15 17
Over 22 24
p-adic value 2
Parallelotope 93
Pell’s equation 106
Period (lattice) 155 161
Period matrix 168
Picard variety 171
Picard’s Theorem 163ff
PID = principal ideal domain 71 87
Place 24 58 92 110
Pole 3 111 138
Positive 31
Prime divisor 58 61 114
Prime element 22 71
Primitive divisor 124
Primitive polynomial 84
Principal divisor 118
Principal divisor class 145
Principal valuation (ring) 19 21
Principle of domination 20
Product formula 92
Puiseux’s theorem 112
Quadratic extension 85
Ramification divisor 113
Ramification index 43
Ramification point 111
Ramified 44 88
Rank 19 32
Rational rank 37 53
Real-valued 19
Regular point 111
Residue 140
Residue class field 20
Residue degree 43
Riemann matrix (pair) 170
Riemann sphere 24
Riemann surface 111 131
Riemann-Roch formula, Theorem 112 144
Riemann’s theorem 125
Roch, G. 144
Schmidt, F.K. 99
Segment, upper, lower 32
Separating element 99
Series, linear 124 128 158
Serre duality theorem 143
Shafarevich, I.R. 108
Specialty index) 126 145
Steinitz, E. 35
Stokes theorem 168
Strong approximation property, theorem 59ff
Subordinate valuation 38
Supernatural number 35 180
Support 42
Symmetry 158
Tamely ramified 81 112
Tensor product 54
Transcendence degree 51
Transcendental 83
Translation 159
Translation invariance 6
Triangle inequality 1 6
Trijection 25
Trivial 19
UFD = unique factorization domain 71
Ultrametric inequality 3
Uniformizer 22 1
UNIT 26
Unit divisor 114
Unit theorem 102
Upper segment 32
Valuated field 19
Valuation 19
Valuation ring, integers 20
Value (at a place) 24 111
Value group 19ff
Volume 94
Weierstrass gap theorem 150
Weierstrass normal form 156
Weierstrass point 150
Whaples, G. 83
Zero 3 111 138
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