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Author:   Henri Lombardi ,  Claude Quitté
Publisher:   Springer
Imprint:   Springer
Edition:   1st ed. 2015
Volume:   20
Dimensions:   Width: 15.50cm , Height: 5.40cm , Length: 23.50cm
Weight:   1.707kg
ISBN:  

9789401799430

ISBN 10:   9401799431
Pages:   996
Publication Date:   04 August 2015
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Examples.- The basic local-global principle and systems of linear equations.- The method of undetermined coefficients.- Finitely presented modules.- Finitely generated projective modules.-Examples.- The basic local-global principle and systems of linear equations.- The method of undetermined coefficients.- Finitely presented modules.- Finitely generated projective modules, 1.- Strictly finite algebras and Galois algebras.- The dynamic method.- Flat modules.- Local rings, or just about.- Finitely generated projective modules, 2.- Distributive lattices, lattice-groups.- Prüfer and Dedekind rings.- Krull dimension.- The number of generators of a module.- The local-global principle.- Extended projective modules.- Suslin’s stability theorem.- Annex.- Constructive logic.

Reviews

The book under review is the faithful English translation of the original French edition published in 2011 under the same title. ... No doubt, the English edition ... will certainly increase both its international significance and its wider popularity among graduate students, researchers, instructors, and interested scientists in general. (Werner Kleinert, zbMATH 1327.13001, 2016)

The book has over 350 well-arranged exercises, together with helpful hints for solution. ... Many methods, like lazy evaluation and dynamic evaluation, are discussed in great detail. ... There is a detailed flow chart on chapter dependencies and the order in which chapters should be read. ... The book will be useful for graduate students, as well as researchers, instructors, and theoretical computer scientists. (Naga Narayanaswamy, Computing Reviews, February, 2016) The book under review is the faithful English translation of the original French edition published in 2011 under the same title. ... No doubt, the English edition ... will certainly increase both its international significance and its wider popularity among graduate students, researchers, instructors, and interested scientists in general. (Werner Kleinert, zbMATH 1327.13001, 2016)

Author Information

Henri Lombardi is a researcher in constructive mathematics, real algebra and algorithmic complexity. Since 2003, with Marie-Françoise Roy and Thierry Coquand, he has developed the international group MAP (Mathematics, Algorithms, Proofs). He has published Épistémologie mathématique, (Ellipse, 2011), and Méthodes matricielles. Introduction à la complexité algébrique, (Springer, 2003, in collaboration with Jounaïdi Abdeljaoued). Claude Quitté is a researcher in effective commutative algebra, computer algebra and computer science. He has published Algorithmique algébrique, (Masson, 1991) in collaboration with Patrice Naudin. Henri Lombardi and Claude Quitté also published together with Maria-Gema Díaz-Toca the book Modules sur les anneaux commutatifs (Calvage & Mounet, 2014).

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