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Prestel A. — Formally P-Adic Fields
Prestel A. — Formally P-Adic Fields

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Название: Formally P-Adic Fields

Автор: Prestel A.

Язык: en

Рубрика: Математика/

Серия: Lecture Notes in Mathematics

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1984

Количество страниц: 176

Добавлена в каталог: 12.09.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\gamma$-Kochen ring      102
$\kappa$-saturated      62
$\mathbb{Z}$ - group      9 85
$\pi$-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
Center      100
Characterization Theorem, p-adic      9
Characterization Theorem, real      4
Coarse valuation      25
Completeness      89
Convex subgroup      14
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
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
Ersov      5
Formally p-adic      7 92
Formally p-adic of type (e, f)      93
Formally p-adic over      93 125
Formally real      4 92
General Embedding Theorem      63
Hensel's lemma      8 20
Henselian      20
Henselization      21
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 algebraic extensions      57
Isomorphism Theorem for p-adic closures      9
Isomorphism Theorem for real closures      4
Kochen      5
Kochen operator      8
Kochen operator, $\pi$-adic      95 122
Kochen operator, $\pi$-adic of type (e, f)      95
Kochen operator, p-adic      92
Kochen ring over      135
Kuhlmann      142
Language of valued fields      83
Language, modified      84
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
p-adic Analog of Hilbert's $17^{th}$ Problem      148—149
p-adic closure      8 33
p-adic Kochen operator of type (e, f)      92
p-adic topology      124
p-adic transfer principle      10
p-adically closed      8 33 84
p-divisibility      6
p-ramification index      13
p-rank      13 83
p-valuation      7
p-valuation of type (e, f)      93
p-valued field      7
p-valued field of p-rank d      13
Place Existence Theorem      125
Place, rational      124
Positive definite      2
Prime element      13
Principal ideal theorem      118
Pruefer ring      117
Puiseux series      16
Quantifier Elimination Theorem      91
Radical element      48
Radical group      48
Radical Structure Theorem      48
Ramification, p-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, Pruefer ring      117
Rule      11
Schreier      4
Sign function      76
Spectral Structure Theorem      114
Subfield Structure of the p-adic closure      59
Substructure completeness      91
Tarski's transfer principle      5
Teichmueller representative set      39
Theorem, Algebraic Embedding Theorem      53
Theorem, Characterization Theorem (p-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 algebraic extensions      57
Theorem, Isomorphism Theorem for p-adic closures      9
Theorem, Isomorphism Theorem for real closures      4
Theorem, Model Completeness Theorem      86
Theorem, Nullstellensatz      143
Theorem, p-adic Analog of Hilbert's $17^{th}$ Problem      148—149
Theorem, Place Existence Theorem      125
Theorem, Principal Ideal Theorem      118
Theorem, Quantifier Elimination Theorem      91
Theorem, Radical Structure Theorem      48
Theorem, Subfield Structure of p-adic closure      59
Totally positive      3
Transfer principle, p-adic      10
Transfer principle, Tarski's      5
Type (e, f)      92 93
Ultra-filter      18
Ultra-power      17
Uniqueness of p-adic closure      37
Unit, level of a unit      45
Universal axiom      83
Valuation, p-valuation      7
Valuation, p-valuation of type (e, f)      93
Zariski topology      124
Zariski's Local Uniformization      142
Zariski-dense      145
Zero support      18
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