Name: Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (en Inglés)
Price: 57.93 USD
Availability: InStock
Author: Yengui, Ihsen
ISBN: 9783319194936

portada Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (en Inglés)

Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (en Inglés)

Formato

Libro Físico

Autor

Ihsen Yengui

Editorial

Springer

Idioma

Inglés

N° páginas

271

Encuadernación

Tapa Blanda

Dimensiones

23.4 x 15.6 x 1.5 cm

Peso

0.40 kg.

ISBN13

9783319194936

Categorías

Ciencia y análisis de datos: generalidades
Lógica matemática
Álgebra
Análisis y captura de datos

Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (en Inglés)

Ihsen Yengui (Autor) · Springer · Tapa Blanda

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Reseña del libro "Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (en Inglés)"

The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented.Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.