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.這本由B. L. van der Waerden 編寫的的近世代數學，是20世紀最暢銷的數學圖書之一。至今，本書已再版10餘次，堪稱是一部經典之作。可以說，幾乎每個研究代數學的人員都直接或間接受本書的影響。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 1 NUMBERS AND SETS
1.1 Sets
1.2 Mappings ,Cardinality
1.3 The Number sequence
1.4 Finite and countable (denumerable)sets
1.5 partitions
Chapter 2 GROUPS
2.1 The concept of a group
2.2 subgrougs
2.3 compleses.cosets
2.4 Isomorphisms and automorphisms
2.5 Homomorphisms ,normal subgroups,and factor groups
Chapter 3 RINGS AND FIELDS
3.1 Rings
3.2 Homomorphism and Isomorphism
3.3 The concept of a field quotients
3.4 Polynomial rings
3.5 Ideals,residue class rings
3.6 divesibility .prime ideals
3.7 Euclidean rings and principal ideal rings
3.8 Factorization
Chapter 4 VECTOR SPACES AND TENSOR SPACES
4.1 Vector spaces
4.2 Dimensional invariance
4.3 The dual vector space
4.4 Linear equations in a skew field
4.5 Linear transformations
4.6 Tensors
4.7 Antisymmetric multilinear forms and determinants
4.8 Tensor products,contraction,and trace
Chapter 5 POLYNOMIALS
5.1 Differentiation
5.2 The zeros of a polynomial
5.3 Interpolation formulae
5.4 Factorixation
5.5 Irrdeucibility criteria
5.6 Factorixation in a finite number of steps
5.7 symmetric functions
5.8 the resultant of two polynomials
5.9 the resultant as a symmetric function of the roots
5.10 partial fraction decomposition
Chapter 6 THEORY OF FIELDS
Chapter 7 CONTINUATION OF GROUP THEORY
Chapter 8 THE GALOIL THEEORY
Chapter 9 ORDERING AND WELL ORDERING OF SETS
Chapter 10 INFINITE FIELD EXTENSIONS
Chapter 11 REAL FIELDS
INDEX
