代數(shù)學(xué)（第1卷）

內(nèi)容概要

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.

書籍目錄

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  partitionsChapter 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 groupsChapter 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  FactorizationChapter 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 traceChapter 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 decompositionChapter 6  THEORY OF FIELDSChapter 7  CONTINUATION OF GROUP THEORYChapter 8  THE GALOIL THEEORYChapter 9  ORDERING AND WELL ORDERING OF SETSChapter 10  INFINITE FIELD EXTENSIONSChapter 11  REAL FIELDSINDEX

編輯推薦

　　本書特色：抽象與具體結(jié)合，理論與應(yīng)用結(jié)合。目前的代數(shù)書，常常單線地朝抽象方向發(fā)展，使讀者--甚至一些數(shù)學(xué)家們--覺(jué)得代數(shù)學(xué)是抽象概念的游戲。各種數(shù)學(xué)理論的平行發(fā)展，到了代數(shù)學(xué)中，取得了整合與統(tǒng)一。

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