Constructive Commutative Algebra - Projective Modules Over Polynomial Rings and Dynamical Groebner Bases (Paperback, 1st ed. 2015)

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 Groebner 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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2138
Release date:	December 2015
First published:	2015
Authors:	Ihsen Yengui
Dimensions:	235 x 155 x 21mm (L x W x T)
Format:	Paperback
Pages:	271
Edition:	1st ed. 2015
ISBN-13:	978-3-319-19493-6
Categories:	Books > Computing & IT > General theory of computing > Mathematical theory of computation Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Promotions
LSN:	3-319-19493-3
Barcode:	9783319194936

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