代数学 第2卷

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