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Inhaltsangabe
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.
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Über die Autorin bzw. den Autor
Dr. Jésus M. Ruiz ist Professor für Mathematik am Institut für Geometrie und Topologie an der Universität Complutense de Madrid.
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The Basic Theory of Power Series
Verlag:
Braunschweig, Wiesbaden, Friedr. Vieweg & Sohn, 1993
ISBN 10: 3528065257
ISBN 13: 9783528065256
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23 x 16 cm. Zustand: Gut. 1. Auflage. IX, 134 Seiten Innen sehr sauberer, guter Zustand. Softcover, mit den üblichen Bibliotheks-Markierungen, Stempeln und Einträgen, innen wie außen, siehe Bilder. (Evtl. auch Kleber- und/oder Etikettenreste, sowie -abdrücke durch abgelöste Bibliotheksschilder). - Paperback with library label on spine. Easy rubbed corners, good condition. Inside with the common library stamps and inscriptions. Otherwise very clean. B15-02-03D|A54 Altersfreigabe FSK ab 0 Jahre Sprache: Englisch Gewicht in Gramm: 260. Bestandsnummer des Verkäufers 62166
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The Basic Theory of Power Series - Advanced Lectures in Mathematics
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Softcover. Zustand: Gut. Ruiz Jesus M. The Basic Theory of Power Series - Advanced Lectures in Mathematics SC - 16 x 23 cm - Verlag: Vieweg, Braunschweig - 1993 - ISBN 3528065257 - 134 Seiten Klappentext: Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert'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 subiects mentioned above usually had to learn about power series within the framework of the vast theory of the subiect. The present book opens another path: One gets acquaintance With power series in a direct and elementary way, and then is given a good box of tools and examples to penetrate any of the subiects mentioned above, and also some others. Zustand: GUT! Einband mit leichten Gebrauchsspuren, innen sauber! Size: 16 x 23 Cm. Buch. Bestandsnummer des Verkäufers 035634
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The Basic Theory of Power Series (Advanced Lectures in Mathematics)
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The Basic Theory of Power Series
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The aim of these notes is to cover the basic algebraic tools and results behind the scenes in the foundations of Real and Complex Analytic Geometry. The author has learned the subject through the works of many mathematicians, to all of whom he is indebted. However, as the reader will immediately realize, he was specially influenced by the writings of S.S. Abhyankar and J .-C. Tougeron. In any case, the presentation of all topics is always as elementary as it can possibly be, even at the cost of making some arguments longer. The background formally assumed consists of: 1) Polynomials: roots, factorization, discriminant; real roots, Sturm's Theorem, formally real fields; finite field extensions, Primitive Element Theorem. 2) Ideals and modules: prime and maximal ideals; Nakayama's Lemma; localiza tion. 3) Integral dependence: finite ring extensions and going-up. 4) Noetherian rings: primary decomposition, associated primes, Krull's Theorem. 5) Krull dimension: chains of prime ideals, systems of parameters; regular systems of parameters, regular rings. These topics are covered in most texts on Algebra and/or Commutative Algebra. Among them we choose here as general reference the following two: - M. Atiyah, I.G. Macdonald: Introduction to Commutative Algebra, 1969, Addison-Wesley: Massachusetts; quoted [A-McD] . - S. Lang: Algebra, 1965, Addison-Wesley: Massachusetts; quoted [L]. 134 pp. Englisch. Bestandsnummer des Verkäufers 9783528065256
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The Basic Theory of Power Series
Verlag:
Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1993, 1993
ISBN 10: 3528065257
ISBN 13: 9783528065256
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Taschenbuch. Zustand: Neu. Neuware -The aim of these notes is to cover the basic algebraic tools and results behind the scenes in the foundations of Real and Complex Analytic Geometry. The author has learned the subject through the works of many mathematicians, to all of whom he is indebted. However, as the reader will immediately realize, he was specially influenced by the writings of S.S. Abhyankar and J .-C. Tougeron. In any case, the presentation of all topics is always as elementary as it can possibly be, even at the cost of making some arguments longer. The background formally assumed consists of: 1) Polynomials: roots, factorization, discriminant; real roots, Sturm's Theorem, formally real fields; finite field extensions, Primitive Element Theorem. 2) Ideals and modules: prime and maximal ideals; Nakayama's Lemma; localiza tion. 3) Integral dependence: finite ring extensions and going-up. 4) Noetherian rings: primary decomposition, associated primes, Krull's Theorem. 5) Krull dimension: chains of prime ideals, systems of parameters; regular systems of parameters, regular rings. These topics are covered in most texts on Algebra and/or Commutative Algebra. Among them we choose here as general reference the following two: ¿ M. Atiyah, I.G. Macdonald: Introduction to Commutative Algebra, 1969, Addison-Wesley: Massachusetts; quoted [A-McD] . ¿ S. Lang: Algebra, 1965, Addison-Wesley: Massachusetts; quoted [L].Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 148 pp. Englisch. Bestandsnummer des Verkäufers 9783528065256
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