代数学 第1卷

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