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Commutative algebra = constructive methods : finite projective modules /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Commutative algebra/ by Henri Lombardi, Claude Quitte.
其他題名:	constructive methods : finite projective modules /
作者:	Lombardi, Henri.
其他作者:	Quitte, Claude.
出版者:	Dordrecht :Springer Netherlands : : 2015.,
面頁冊數:	xl, 994 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Commutative algebra. -
電子資源:	http://dx.doi.org/10.1007/978-94-017-9944-7
ISBN:	9789401799447 (electronic bk.)

Commutative algebra = constructive methods : finite projective modules /
Lombardi, Henri.

Commutative algebraconstructive methods : finite projective modules /[electronic resource] :by Henri Lombardi, Claude Quitte. - Dordrecht :Springer Netherlands :2015. - xl, 994 p. :ill., digital ;24 cm. - Algebra and applications,v.201572-5553 ;. - Algebra and applications ;v.17..

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.

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.

ISBN: 9789401799447 (electronic bk.)

Standard No.: 10.1007/978-94-017-9944-7doiSubjects--Topical Terms:

672047
Commutative algebra.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Commutative algebra = constructive methods : finite projective modules /
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520 $a 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.
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