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范德瓦尔登 编 / 世界图书出版公司 / 2007-10 / 平装
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代数学(第2卷)
《代数学(第2卷)》特色:抽象与具体结合,理论与应用结合。目前的代数书,常常单线地朝抽象方向发展,使读者--甚至一些数学家们--觉得代数学是抽象概念的游戏。各种数学理论的平行发展,到了代数学中,取得了整合与统一。
Chapter 12 LINEAR ALGEBRA 12.1 Modules over a ring 12.2 Modules over euclidean rings ,elementary divisors 12.3 The fundamental theorem of abelian groups 12.4 Representations and represecntation modules 12.5 Normal forms of a matrix in a commutative field 12.6 Elementary divisors and characteeristic functions 12.7 Quadratic and hermitian forms 12.8 Antisymmetric bilinear forms Chapter 13 ALGEBRAS 13.1 Direct sums and intersections 13.2 Examples of algebras 13.3 Products and crossed products 13.4 Algebras as groups with operators ,modules and representations 13.5 The large and small radicals 13.6 The star product 13.7 Rings with minimal condition 13.8 TWO-sided decompositions and center decomposition 13.9 Simple and primitive rings 13.10 The endomorphism ring of a direct sum 13.11 structure theorems for semisimple and simple rings 13.12 The behavior of algebras under extension of the base field Chapter 14 REPRESENTATION THE ORY OF GROUPS AND ALGEBRAS 14.1 Statement of the problem 14.2 Representation of algebras 14.3 Representation of the center 14.4 traces and characters 14.5 representations of finite groups 14.6 Group characters 14.7 The reprsedntations of the symmetric groups 14.8 Semigroups of linear and products of algebras 14.9 Double modules and products of algebras 14.10 The splitting fields of a simple algebra 14.11 The brauer group.factor systems Chapter 15 GENERAL IDEAL THEORY OF COMMUTATIVE RINGS 15.1 Noetherian rings 15.2 Products and quotients of ideals 15.3 Prime ideals and primary ideals 15.4 The general decomposition theorem 15.5 The general decomposition theorem 15.6 Isolatde components and symbolic powers 15.7 Theory of relatively prime ideals 15.8 Single-primed ideals 15.9 Quotient rings 15.10 THE intersecrion of all porers of and ideal 15.11 The length of q primary ideal ,chains of primary ideals in noetherian rings Chapter16 THEORY OF POLYNOMIAL IDEALS Chapter17 INTEGRAL ALGEBRAIC ELEMENTS Chapter18 FIELDS WITH VALUATIONS Chapter19 ALGEBRAIC FUNCTIONS OF ONE VARIABLE Chapter20 TOPOLOGICAL ALGEBRA INDEX
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