A. Prestel, P. Roquette — Formally p-adic Fields :: Электронная библиотека попечительского совета мехмата МГУ

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A. Prestel, P. Roquette — Formally p-adic Fields

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Название: Formally p-adic Fields

Авторы: A. Prestel, P. Roquette

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 179

Добавлена в каталог: 13.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-adic Analog of Hilbert’s $17^{th}$ Problem      148 149
-adic closure      8 33
-adic Kochen operator of type (e,f)      92
-adic topology      124
-adic transfer principle      10
-adically closed      8 33 84
-divisibility      6
-ramification index      13
-rank      13 83
-valuation      7
-valuation of type (e,f)      93
-valued field      7
-valued field of -rank d      13
$\gamma$ — Kochen ring      102
$\kappa$ -saturated      6 2
$\mathbb{Z}$ -group      9 8 5
$\pi$ -adic Kochen operator      122
$\pi$ -adic Kochen operator of type (e,f)      95
(relative) initial index      23 94
Absolute value      1
Algebraic Embedding Theorem      53
Artin      2
Ax      5
Axiom, universal      83
Base field      93
Basic subset      125
Bezout ring      117
Canonical decomposition      24
Characterization Theorem, -adic      9
Characterization Theorem, real      4
Coarse valuation      25
Completeness      89
Convex subgroup      1 4
Core field      26
Core valuation      27
Decidability      5 87 89
Decomposition, canonical      24
Defect      29
Defining relation      52
Definite, integral      123 144 149
Definite, positive      2
Denter      100
Dimension (of a place)      123
Eisenstein polynomial      39
Elementary equivalence theorem      90
Elementary extension      86
Embedding Theorem for regular extensions      65
Embedding Theorem, Algebraic      53
Er $\check{s}$ ov      5
Formally -adic      7 92
Formally -adic of type (e,f)      93
Formally -adic over      93 125
Formally real      4 92
General Embedding Theorem      63
Henselian      20
Henselization      21
Hensel’s Lemma      8 20
Hilbert’s $17^{th}$ Problem      2
Holomorphic at      134
Holomorphy ring      104 134
Immediate extension      21
Initial index      23 94
Integral definite      123 144 149
Isomorphism Theorem for -adic closures      9
Isomorphism Theorem for algebraic extensions      57
Isomorphism Theorem for real closures      4
Kochen      5
Kochen operator      8
Kochen operator, -adic      92
Kochen operator, $\pi$ -adic      95 122
Kochen operator, $\pi$ -adic of type (e,f)      95
Kochen ring over      135
Kuhlmann      142
Language, modified      84
Language, of valued fields      83
Laurent series (formal)      16
Level of a unit      45
lexicographical ordering      15

MacIntyre      91
McKenna      149
Merckel’s Lemma      102 135 153
Model completeness (of real closed fields)      5
Model Completeness Theorem      86
Modified language      84
Nakayama’s Lemma      111
Newton’s Lemma      20
Non-principal ultra filter      18
Nullstellensatz      143
Ordering      2
Place Existence Theorem      125
Place, rational      124
Positive definite      2
Priifer ring      117
Prime element      13
Principal ideal theorem      118
Puiseux series      16
Quantifier Elimination Theorem      91
Radical element      48
Radical group      48
Radical Structure Theorem      48
Ramification, -ramification index      13
Ramification, relative ramification index      23
Rational place      124
Real closed      4
Real closure      4
Regular extension      64
Relation, defining relation      52 112
Relative residue degree      94
Relative type      94
Residue degree      15
Riemann space      124
Ring, $\gamma$ — Kochen ring      102
Ring, Bezout ring      117
Ring, holomorphy ring      104 134
Ring, Kochen ring      135
Ring, Pr $\ddot{u}$ fer ring      117
Rule      11
Schreier      4
Sign function      76
Spectral Structure Theorem      114
Subfield Structure of the -adic closure      59
Substructure completeness      91
Tarski’s Transfer Principle      5
Teichm $\ddot{u}$ ller representative set      39
Theorem, -adic Analog of Hilbert’s $17^{th}$ Problem      148 149
Theorem, Algebraic Embedding Theorem      53
Theorem, Characterization Theorem (-adic)      9
Theorem, Characterization Theorem (real)      4
Theorem, Elementary Equivalence Theorem      90
Theorem, Embedding Theorem for regular extensions      65
Theorem, General Embedding Theorem      63
Theorem, Isomorphism Theorem for -adic closures      9
Theorem, Isomorphism Theorem for algebraic extensions      57
Theorem, Isomorphism Theorem for real closures      4
Theorem, Model Completeness Theorem      86
Theorem, Nullstellensatz      143
Theorem, Place Existence Theorem      125
Theorem, Principal Ideal Theorem      118
Theorem, Quantifier Elimination Theorem      91
Theorem, Radical Structure Theorem      48
Theorem, Subfield Structure of -adic closure      59
Totally positive      3
Transfer principle, -adic      10
Transfer principle, Tarski’s      5
Type (e,f)      92 93
Ultra-filter      18
Ultra-power      17
Uniqueness of -adic closure      37
Unit, level of a unit      45
Universal axiom      83
Valuation, -valuation      7
Valuation, -valuation of type (e,f)      93
Zariski topology      124
Zariski-dense      145
Zariski’s Local Uniformization      142
Zero support      18

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