商品簡介
The abstract,formaloraxiomaticdirection,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.這本書由B. L. van der Waerden 編寫的的近世代數學，部分的依賴於上個世紀20年代Emmy Noether 和 Emil Artin的講演稿。第一次出版是在20世紀30年代，首次建立起了代數學研究的框架，將抽象代數引進了數學領域。是20世紀最暢銷的數學類書之一。至今，這本書已經再版了10來次，現在仍然很受歡迎，可以說，幾乎每個研究代數學的人都直接或間接的受它的影響，堪稱是一部經典之作。本書分為上下兩卷，在第一卷有一個讀書嚮導，列出了這兩卷的所有的章以及它們之間的相互關係，這對讀者理解這本書和瞭解代數學的基本框架都有很大的幫助。內容由數論與集合、群、環、理想以及域構成並展開。
目次：數論和集合；群；環和域；向量空間和張量空間；多項式；域理論；群理論的拓展；伽羅瓦理論；有序和最好序集合；無限域擴張；實域；線性代數；代數學；群和代數學的表示論；交換環的一般理想理論；多項式理想理論；整代數元；有值域；單變量代數函數；拓撲代數。
目次
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
