عنوان

Introduction to Algebra

(Number (ISBN

9400981791

(Number (ISBN

9400981813

(Number (ISBN

9789400981799

(Number (ISBN

9789400981812

Number

b593955

Title Proper

Introduction to Algebra

General Material Designation

[Book]

First Statement of Responsibility

by R. Kochendörffer.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands

Date of Publication, Distribution, etc.

1981

Text of Note

1. Basic concepts.- 1.1. Sets.- 1.2. Relations.- 1.3. Mappings.- 1.4. Operations.- 1.5. Algebraic systems.- Exercises.- 2. The integers.- 2.1. The natural numbers and the integers.- 2.2. Divisibility. Prime numbers.- 2.3. The greatest common divisor.- 2.4. Prime factorization.- 2.5. Congruences. Residue classes.- 2.6. The residue class ring.- 2.7. Simultaneous congruences. Euler's function.- Exercises.- 3. Groups.- 3.1. Semigroups.- 3.2. Groups.- 3.3. Isomorphisms. Automorphisms.- 3.4. Embedding of abelian semigroups in groups.- 3.5. Subgroups.- 3.6. Cyclic groups.- 3.7. Homomorphisms.- 3.8. Subnormal series.- 3.9. Direct products.- 3.10. Permutation groups.- 3.11. Sylow subgroups and p-groups.- 3.12. Endomorphisms and operators.- 3.13. Vector spaces. Modules.- Exercises.- 4. Rings. Integral domains.- 4.1. Definitions and examples.- 4.2. Homomorphisms.- 4.3. Commutative rings. Integral domains.- 4.4. Principal ideal rings.- 4.5. Euclidean rings.- 4.6. Fields of quotients.- 4.7. Prime fields. Characteristic.- Exercises.- 5. Polynomials.- 5.1. Polynomials in one indeterminate.- 5.2. Polynomials over fields.- 5.3. Polynomials over integral domains..- 5.4. Roots. The derivative.- 5.5. Polynomials in several indeterminates.- 5.6. Symmetric polynomials.- 5.7. The resultant and the discriminant.- Exercises.- 6. Fields.- 6.1. Adjunction.- 6.2. Algebraic extension fields.- 6.3. Construction of extension fields.- 6.4. Normal extensions.- 6.5. Separable and inseparable extensions.- 6.6. Galois theory.- 6.7. Cyclotomic fields.- 6.8. Galois fields.- Exercises.- 7. Galois theory of equations.- 7.1. The Galois group of a polynomial.- 7.2. Solubility of equations by radicals.- 7.3. Quadratic, cubic, and quartic equations.- 7.4. Constructions by ruler and compass.- Exercises.- 8. Order and valuations.- 8.1. Ordered fields.- 8.2. Formally real fields.- 8.3. Valuations.- Exercises.- 9. Modules.- 9.1. Elementary divisors.- 9.2. Modules over principal ideal rings.- 9.3. Endomorphisms of vector spaces.- 9.4. Finiteness conditions.- 9.5. Algebraic integers.- Exercises.- 10. Algebras.- 10.1. Basic definitions.- 10.2. The radical.- 10.3. Semi-simple rings.- 10.4. Simple rings.- 10.5. Division algebras over the field of the real numbers.- 10.6. Representation modules.- 10.7. Representations of semi-simple algebras.- Exercises.- 11. Lattices.- 11.1. Lattices and partially ordered sets.- 11.2. Modular lattices.- 11.3. Distributive lattices.- Exercises.

Mathematics.

Class number

Book number

by R. Kochendörffer.

R Kochendörffer

Electronic name

[Book]

Y