Basic Theory of Power Series

Häftad, Engelska, 1993

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This volume covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any branches of mathematics, particularly in complex and in real analytic geometry, in commutative algebra, in algebraic geometry and in real algebraic geometry. In particular it presents Rueckert's complex nullstellensatz, Risler's real nullstellensatz, Tougeron's implicit function theorem and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. This had the advantage that he sees many theorems about power series as special instances of more general facts, but on the other hand made it highly time consuming to understand all these theorems. The present book opens another path - one gets acquainted with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, as well as some others.

Produktinformation

Utgivningsdatum1993-01-01
Mått162 x 229 x 9 mm
Vikt241 g
FormatHäftad
SpråkEngelska
SerieAdvanced Lectures in Mathematics
Antal sidor134
Upplaga1993
FörlagFriedrich Vieweg & Sohn Verlagsgesellschaft mbH
ISBN9783528065256

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

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.