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 wellarranged 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 localglobal principle and systems of linear equations The method of undetermined coefficients Finitely presented modules Finitely generated projective modules.Examples The basic localglobal 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, latticegroups Prüfer and Dedekind rings Krull dimension The number of generators of a module The localglobal principle Extended projective modules Suslin’s stability theorem Annex Constructive logic. Examples The basic localglobal principle and systems of linear equations The method of undetermined coefficients Finitely presented modules Finitely generated projective modules.Examples The basic localglobal principle and systems of linear equations