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.
作者簡介
暫缺《代數(shù)學（第2卷 英文版）》作者簡介
圖書目錄
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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