Commutative algebra [electronic resource] : constructive methods : finite projective modules / Henri Lombardi, Claude Quitté.

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Commutative algebra [electronic resource] : constructive methods : finite projective modules / Henri Lombardi, Claude Quitté.

9789401799447 electronic book
940179944X electronic book
9789401799430

Dordrecht : Springer, 2015.

English

Translated from the French.

1 online resource (xlix, 996 pages) : illustrations.

QA251.3

512/.44

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.

"English translation by Tania K. Roblot."

Includes bibliographical references and index.

Access limited to authorized users.

Online resource; title from PDF title page (SpringerLink, viewed July 31, 2015).

Algebras and applications ; volume 20.

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