代數(shù)學(xué)（第2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 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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