Commutative Algebra: Constructive Methods: Finite Projective Modules: 20 - Brossura

Lombardi, Henri; Quitt, Claude

Brossura

ISBN 10: 940240399X ISBN 13: 9789402403992

Casa editrice: Springer Nature, 2016

Riassunto

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, Prüfer 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.

Su questo libro

Informazioni sull?autore

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 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 Quitté 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 Quitté also published together with Maria-Gema Díaz-Toca the book Modules sur les anneaux commutatifs (Calvage & Mounet, 2014).

Dalla quarta di copertina

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, Prüfer 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.

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 940240399X
• ISBN 13: 9789402403992
• Rilegatura: Copertina flessibile
• Numero di pagine: 1048
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania