Commutative Algebra: Constructive Methods [electronic resource] : Finite Projective Modules / by Henri Lombardi, Claude Quitté.
Contributor(s): Quitté, Claude [author.] | SpringerLink (Online service)Material type: TextSeries: Algebra and Applications: 20Publisher: Dordrecht : Springer Netherlands : Imprint: Springer, 2015Description: XLIX, 996 p. 80 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9789401799447Subject(s): Mathematics | Computer science -- Mathematics | Commutative algebra | Commutative rings | Algebra | Field theory (Physics) | Matrix theory | Mathematics | Commutative Rings and Algebras | Field Theory and Polynomials | Linear and Multilinear Algebras, Matrix Theory | Symbolic and Algebraic ManipulationAdditional physical formats: Printed edition:: No titleDDC classification: 512.44 LOC classification: QA251.3Online resources: Click here to access online
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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.