Commutative Algebra: Constructive Methods: Finite Projective Modules (Algebra and Applications 20 1st ed. 2015)

Commutative Algebra: Constructive Methods: Finite Projective Modules (Algebra and Applications 20 1st ed. 2015)

By: Henri Lombardi (author), Claude Quitte (author)Hardback

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Description

Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prufer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.

About Author

Henri Lombardi is a researcher in constructive mathematics, real algebra and algorithmic complexity. Since 2003, with Marie-Francoise Roy and Thierry Coquand, he has developed the international group MAP (Mathematics, Algorithms, Proofs). He has published E piste mologie mathe matique, (Ellipse, 2011), and Me thodes matricielles. Introduction a la complexite alge brique, (Springer, 2003, in collaboration with Jounai di Abdeljaoued). Claude Quitte is a researcher in effective commutative algebra, computer algebra and computer science. He has published Algorithmique alge brique, (Masson, 1991) in collaboration with Patrice Naudin. Henri Lombardi and Claude Quitte also published together with Maria-Gema Diaz-Toca the book Modules sur les anneaux commutatifs (Calvage & Mounet, 2014).

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.- Prufer 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.

Product Details

  • ISBN13: 9789401799430
  • Format: Hardback
  • Number Of Pages: 996
  • ID: 9789401799430
  • ISBN10: 9401799431
  • edition: 1st ed. 2015

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