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＜電子ブック＞
Commutative Algebra: Constructive Methods : Finite Projective Modules / by Henri Lombardi, Claude Quitté
(Algebra and Applications. ISSN:21922950 ; 20)

版	1st ed. 2015.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2015
大きさ	XLIX, 996 p. 80 illus : online resource
著者標目	*Lombardi, Henri author Quitté, Claude author SpringerLink (Online service)
件　名	LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebras, Linear LCSH:Computer science—Mathematics FREE:Commutative Rings and Algebras FREE:Field Theory and Polynomials FREE:Linear Algebra FREE:Symbolic and Algebraic Manipulation
一般注記	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 -- Prüfer 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, 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 HTTP:URL=https://doi.org/10.1007/978-94-017-9944-7

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