代数学（第2卷）
2007-10
北京世图
范德瓦尔登
284
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The "abstract,""formal"or"axiomatic"direction,to which the fresh impetus in algebra is euc ,haw led ,haw led to a numbe of new formulations of ideas,insight into new interrelations,and far-reaching results results,especially in group theory ,field theory,valuation theory, ideal theory,and the theory of hypercomplex numbers.The principal objective of this reason ,genreral concepts and methods stand in the foregorund ,particular results which properly belong to classical algebra must also be give appropriate consideration within the framrwork of the modern development.
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 formsChapter 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 fieldChapter 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 systemsChapter 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 ringsChapter16 THEORY OF POLYNOMIAL IDEALSChapter17 INTEGRAL ALGEBRAIC ELEMENTSChapter18 FIELDS WITH VALUATIONSChapter19 ALGEBRAIC FUNCTIONS OF ONE VARIABLEChapter20 TOPOLOGICAL ALGEBRAINDEX
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代数学的经典之作
很好很好的书籍，值得每个感兴趣的人好好读读
范德瓦尔登，真正的好书，这还用说什么呢？要读就读名著。
很好的书,如果是原版就完美了