大葉大學圖書館 |

Commutative algebra[electronic resource] :constructive methods : finite projective modules /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512.44
書名/作者:	Commutative algebra : constructive methods : finite projective modules // by Henri Lombardi, Claude Quitte.
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.
標題:	Mathematics.
標題:	Commutative Rings and Algebras.
標題:	Field Theory and Polynomials.
標題:	Linear and Multilinear Algebras, Matrix Theory.
標題:	Symbolic and Algebraic Manipulation.
ISBN:	9789401799447 (electronic bk.)
ISBN:	9789401799430 (paper)
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-94-017-9944-7

Commutative algebra[electronic resource] :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:

510987
Commutative algebra.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Commutative algebra[electronic resource] :constructive methods : finite projective modules /
LDR:03017nam a2200325 a 4500 001 443182
003 DE-He213
005 20160223153936.0
006 m d
007 cr nn 008maaau
008 160715s2015 ne s 0 eng d
020 $a 9789401799447 (electronic bk.)
020 $a 9789401799430 (paper)
024 7 $a 10.1007/978-94-017-9944-7 $2 doi
035 $a 978-94-017-9944-7
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA251.3
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512.44 $2 23
090 $a QA251.3 $b .L842 2015
100 1 $a Lombardi, Henri. $3 633609
245 1 0 $a Commutative algebra $h [electronic resource] : $b constructive methods : finite projective modules / $c by Henri Lombardi, Claude Quitte.
260 $a Dordrecht : $b Springer Netherlands : $b Imprint: Springer, $c 2015.
300 $a xl, 994 p. : $b ill., digital ; $c 24 cm.
490 1 $a Algebra and applications, $x 1572-5553 ; $v v.20
505 0 $a 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.
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.
650 0 $a Commutative algebra. $3 510987
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Commutative Rings and Algebras. $3 464925
650 2 4 $a Field Theory and Polynomials. $3 467525
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 464949
650 2 4 $a Symbolic and Algebraic Manipulation. $3 465559
700 1 $a Quitte, Claude. $3 633610
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Algebra and applications ; $v v.17. $3 465830
856 4 0 $u http://dx.doi.org/10.1007/978-94-017-9944-7
950 $a Mathematics and Statistics (Springer-11649)