portada The Basic Theory of Power Series (en Inglés)

The Basic Theory of Power Series (en Inglés)

Formato

Libro Físico

Autor

Jesús M. Ruiz

Editorial

Vieweg+teubner Verlag

Año

2012

Idioma

Inglés

N° páginas

134

Encuadernación

Tapa Blanda

ISBN

3528065257

ISBN13

9783528065256

Categorías

Geometría

The Basic Theory of Power Series (en Inglés)

Jesús M. Ruiz (Autor) · Vieweg+teubner Verlag · Tapa Blanda

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Reseña del libro "The Basic Theory of Power Series (en Inglés)"

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].