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Mathematics - Geometry & Topology | The Basic Theory of Power Series

The Basic Theory of Power Series

Ruiz, Jesús M.

1993, X, 134p.

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Zielgruppe
1. Studenten der Mathematik im Hauptstudium 2. Dozenten und Professoren der Mathematik 3. Institute 4. Bibliotheken

Über den Autor/Hrsg
Dr. Jésus M. Ruiz ist Professor für Mathematik am Institut für Geometrie und Topologie an der Universität Complutense de Madrid.

Content Level » Upper undergraduate

Related subjects » Geometry & Topology

Table of contents 

I Power Series.- 1 Series of Real and Complex Numbers.- 2 Power Series.- 3 Rückert’s and Weierstrass’s Theorems.- II Analytic Rings and Formal Rings.- 1 Mather’s Preparation Theorem.- 2 Noether’s Projection Lemma.- 3 Abhyankar’s and Rückert’s Parametrization.- 4 Nagata’s Jacobian Criteria.- 5 Complexification.- III Normalization.- 1 Integral Closures.- 2 Normalization.- 3 Multiplicity in Dimension 1.- 4 Newton-Puiseux’s Theorem.- IV Nullstellensatze.- 1 Zero Sets and Zero Ideals.- 2 Rückert’s Complex Nullstellensatz.- 3 The Homomorphism Theorem.- 4 Risler’s Real Nullstellensatz.- 5 Hilbert’s 17th Problem.- V Approximation Theory.- 1 Tougeron’s Implicit Functions Theorem.- 2 Equivalence of Power Series.- 3 M. Artin’s Approximation Theorem.- 4 Formal Completion of Analytic Rings.- 5 Nash Rings.- VI Local Algebraic Rings.- 1 Local Algebraic Rings.- 2 Chevalley’s Theorem.- 3 Zariski’s Main Theorem.- 4 Normalization and Completion.- 5 Efroymson’s Theorem.- Bibliographical Note.

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