04847nam 22007695 450 991029977430332120220516172424.094-017-9944-X10.1007/978-94-017-9944-7(CKB)3710000000452278(EBL)3567869(SSID)ssj0001534638(PQKBManifestationID)11855995(PQKBTitleCode)TC0001534638(PQKBWorkID)11494630(PQKB)11699470(DE-He213)978-94-017-9944-7(MiAaPQ)EBC3567869(PPN)187690065(EXLCZ)99371000000045227820150722d2015 u| 0engur|n|---|||||txtccrCommutative algebra: constructive methods finite projective modules /by Henri Lombardi, Claude Quitté1st ed. 2015.Dordrecht :Springer Netherlands :Imprint: Springer,2015.1 online resource (1033 p.)Algebra and Applications,1572-5553 ;20Description based upon print version of record.94-017-9943-1 Includes bibliographical references and index.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.Algebra and Applications,1572-5553 ;20Commutative algebraCommutative ringsAlgebraField theory (Physics)Matrix theoryComputer science—MathematicsCommutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Field Theory and Polynomialshttps://scigraph.springernature.com/ontologies/product-market-codes/M11051Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Symbolic and Algebraic Manipulationhttps://scigraph.springernature.com/ontologies/product-market-codes/I17052Commutative algebra.Commutative rings.Algebra.Field theory (Physics).Matrix theory.Computer science—Mathematics.Commutative Rings and Algebras.Field Theory and Polynomials.Linear and Multilinear Algebras, Matrix Theory.Symbolic and Algebraic Manipulation.512.24Lombardi Henriauthttp://id.loc.gov/vocabulary/relators/aut755733Quitté Claudeauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299774303321Commutative Algebra: Constructive Methods2546584UNINA