LEADER 04847nam 22007695 450 001 9910299774303321 005 20220516172424.0 010 $a94-017-9944-X 024 7 $a10.1007/978-94-017-9944-7 035 $a(CKB)3710000000452278 035 $a(EBL)3567869 035 $a(SSID)ssj0001534638 035 $a(PQKBManifestationID)11855995 035 $a(PQKBTitleCode)TC0001534638 035 $a(PQKBWorkID)11494630 035 $a(PQKB)11699470 035 $a(DE-He213)978-94-017-9944-7 035 $a(MiAaPQ)EBC3567869 035 $a(PPN)187690065 035 $a(EXLCZ)993710000000452278 100 $a20150722d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCommutative algebra: constructive methods $efinite projective modules /$fby Henri Lombardi, Claude Quitté 205 $a1st ed. 2015. 210 1$aDordrecht :$cSpringer Netherlands :$cImprint: Springer,$d2015. 215 $a1 online resource (1033 p.) 225 1 $aAlgebra and Applications,$x1572-5553 ;$v20 300 $aDescription based upon print version of record. 311 $a94-017-9943-1 320 $aIncludes bibliographical references and index. 327 $aExamples -- 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. 330 $aTranslated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors, and theoretical computer scientists. 410 0$aAlgebra and Applications,$x1572-5553 ;$v20 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebra 606 $aField theory (Physics) 606 $aMatrix theory 606 $aComputer science?Mathematics 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aAlgebra. 615 0$aField theory (Physics). 615 0$aMatrix theory. 615 0$aComputer science?Mathematics. 615 14$aCommutative Rings and Algebras. 615 24$aField Theory and Polynomials. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aSymbolic and Algebraic Manipulation. 676 $a512.24 700 $aLombardi$b Henri$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755733 702 $aQuitté$b Claude$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299774303321 996 $aCommutative Algebra: Constructive Methods$92546584 997 $aUNINA