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
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.
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