Advanced Lectures in Mathematics

The Basic Theory of Power Series

Authors: Ruiz, Jesús M.

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About this Textbook

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].

About the authors

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

Buy this book

Softcover $119.00
price for USA
  • ISBN 978-3-528-06525-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Basic Theory of Power Series
Authors
Series Title
Advanced Lectures in Mathematics
Copyright
1993
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
Softcover ISBN
978-3-528-06525-6
Series ISSN
0932-7134
Edition Number
1
Number of Pages
X, 134
Topics