Title: Commutative Algebra: Constructive Methods: Finite Projective Modules (eng)
Publisher: Springer
Publication Date: 2015
Language: English
ISBN 10: 9401799431
ISBN 13: 9789401799430
Binding: Hardcover
Condition: new
Weight: 1.59 kilograms

About this title

Synopsis

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, Pr�fer 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 the Author

Henri Lombardi is a researcher in constructive mathematics, real algebra and algorithmic complexity. Since 2003, with Marie-Fran�oise Roy and Thierry Coquand, he has developed the international group MAP (Mathematics, Algorithms, Proofs). He has published �pist�mologie math�matique, (Ellipse, 2011), and M�thodes matricielles. Introduction � la complexit� alg�brique, (Springer, 2003, in collaboration with Jouna�di Abdeljaoued).

Claude Quitt� is a researcher in effective commutative algebra, computer algebra and computer science. He has published Algorithmique alg�brique, (Masson, 1991) in collaboration with Patrice Naudin.

Henri Lombardi and Claude Quitt� also published together with Maria-Gema D�az-Toca the book Modules sur les anneaux commutatifs (Calvage & Mounet, 2014).

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