Commutative Algebra: Constructive Methods : Finite Projective Modules

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Commutative Algebra: Constructive Methods : Finite Projective Modules

フォーマット:
電子ブック
責任表示:
by Henri Lombardi, Claude Quitté
本文言語:
英語
出版情報:
Dordrecht, Netherlands. 2015-. Springer Netherlands,Imprint: Springer
シリーズ:
Algebra and Applications; 20
概要:
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. 続きを見る
目次:
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.
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
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