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Ruiz J.M. — The basic theory of power series
Ruiz J.M. — The basic theory of power series



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Название: The basic theory of power series

Автор: Ruiz J.M.

Язык: en

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 134

Добавлена в каталог: 05.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
2-real domain      42
Abhyankar's Parametrization      29
Algebraic power series      106
Algebraictry of an isolated hypcrsurface singularity      92
Anaiyticity of the function associated to convergent power series      10
Analytic completion of a local algebraic ring      111
Analytic completion of a Nash ring      109
Analytic homomorphism      16
Analytic ring      16
Analyticity of integral closures      49
Annihilator of a modulo      38
Artin — Schreier's Criterion      80
Birational equivalence to a hypersurface      30
Branches of a 1-dimensional reduced analytic ring      53
Chain rule      9
Chevalley's Theorem      112
Classical Implicit Functions Theorem      36
Classical Inverse Function Theorem      36
Coefficient field      16 109 110
Completion of a local ordering      125ff
Completion of the normalization of a local algebraic domain      122ff
Completion of the normalization of an analytic ring      104
Complexification      39
Conjugation      39ff
Contractive map      12
Convergent power series      4
Convergent Puiseux series      59
Convex ideal      125
Derivatives of a power series      9ff
Derivatives of an algebraic power series      107
Distinguished polynomial      11
Domain of a power series      4
Efroymson's Theorem      129
Equidimensionality Jacobinn Criterion      37
Equivalent power series      91
Factorization of a distinguished polynomial      22
Finite homomorphism      18
Finitehess of integral closures      27
Fixed point theorem      15
Flatness      100 112
Formal completion of a local algebraic ring      111
Formal completion of a Nash ring      109
Formal completion of an analytic ring      99
Formal homomorphism      16
Formal power series      4
Formal Puiseux series      58
Formal ring      16
Formally real domain      73
Function associated to a convergent power series      5
Function associated to a formal power series      64
Generic changes of coordinates      25
Geometric characterization of dimension in the complex case      70
Geometric characterization of finiteness in the complex case      70
Height of an ideal      22
Hensel's lemma      14
Hessian matrix      72
Hilbert's 17th Problem for power series with real coefficients      81
Homomorphism theorem      74
Hypersurface singularity      71
Identity Principle      11
Infinitesimal element      64 126
Invertthio convergent power series      9
Invertthio formal power series      7
Isolated hypersurface singularity      71
Isolated singularity      67
Iterated series      3
Jacobian ideal      31
Leibnitz formula      9
Local algebraic homomorphism      110
Local algebraic ring      110
Local ordering      125
Local Parametrization Theorem      35
Locally real domain      126
M.Artin's Approximation Theorem      94
Mather's Finitehess Theorem      18
Milnor number      72
Morse singularity      72
Morse's lemma      93
Motzkin's counterexample      84
Multiplicity compared through normalization      54ff
Multiplicity of a 1-dimensional reduced analytic ring      53
Multiplicity of a planar ring      56
Nagata's comparison results      101ff
Nash completion of a local algebraic ring      111
Nash homomorphism      109
Nash ring      109
Newton-Puiseux's Theorem      61
Noether's Projection Lemma      24
Normal analytic (rcsp. formal) ring      49
Normalization of a 1-dimensional reduced analytic ring      54
Normalization of a local algebraic domain      120
Normalization of a reduced aualytic ring      49 51
Normalization of the complexification of a reduced analytic (resp. formal) ring over the reals      52
Operations with power series      6ff
Order of a power series      4
Ordering of a domain      73
Ordering of the ring of Puiseux series over the reals      73
Positive semidefinite power series      81
Positive semidefinite power series in two indeterminates      85
Primitive Element Theorem      24
Quadratic transform      57ff
Quasifinite homomorphism      18
Real radical      79
Reduced ring      41
Regular point of dimension 1 of a zero set      67
Regular power series      11
Regular systems of parameters of a ring of power series      29 35
Regularity ideal      31
Regularity Jacobian Criterion      32
Risler's Nullstellensatz      78
Roots of invertible power series      37
Rueckcrt's Parametrization      27ff
Rueckert's Division Theorem      11
Rueckert's Division Theorem for algebraic power series      108
Rueckert's Nullstellensatz      68
Schwartz Rule      9
Serre's criterion      105
Singular point of dimension 1 of a zero set      67
Standard Sturm's sequence      77
Sturm's theorem      77
Substitution of algebratic power series      106i'
Substitution of power series      7
Sum of a series      1
Summahie family of power series      6
Taylor expansion      9
Tougeron's Implicit Functions Theorem      89
Transversal changes of coordinates      22ff
Uniform convergence of a power series      4
Weierstrass's Preparation Theorem      14
Whitney's umbrella      78
Zariski's Condition D      115
Zariski's main theorem      117
Zero idel      65
Zero set      64
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