Algebra / by Thomas W. Hungerford.

Format:

Book

Author/Creator:

Hungerford, Thomas W., author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 0072-5285 ; 73.

Graduate Texts in Mathematics, 0072-5285 ; 73

Language:

English

Subjects (All):

Algebra.

Local Subjects:

Algebra.

Physical Description:

1 online resource (XXIV, 504 pages).

Edition:

First edition 1974.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1974.

System Details:

text file PDF

Summary:

Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.

Contents:

Introduction: Prerequisites and Preliminaries

1. Logic

2. Sets and Classes

3. Functions

4. Relations and Partitions

5. Products

6. The Integers

7. The Axiom of Choice, Order and Zorn's Lemma

8. Cardinal Numbers

I: Groups

1. Semigroups, Monoids and Groups

2. Homomorphisms and Subgroups

3. Cyclic Groups

4. Cosets and Counting

5. Normality, Quotient Groups, and Homomorphisms

6. Symmetric, Alternating, and Dihedral Groups

7. Categories: Products, Coproducts, and Free Objects

8. Direct Products and Direct Sums

9. Free Groups, Free Products, Generators and Relations

II: The Structure of Groups

1. Free Abelian Groups

2. Finitely Generated Abelian Groups

3. The Kruli-Schmidt Theorem

4. The Action of a Group on a Set

5. The Sylow Theorems

6. Classification of Finite Groups

7. Nilpotent and Solvable Groups

8. Normal and Subnormal Series

III: Rings

1. Rings and Homomorphisms

2. Ideals

3. Factorization in Commutative Rings

4. Rings of Quotients and Localization

5. Rings of Polynomials and Formal Power Series

6. Factorization in Polynomial Rings

IV: Modules

1. Modules, Homomorphisms and Exact Sequences

2. Free Modules and Vector Spaces

3. Projective and Injective Modules

4. Horn and Duality

5. Tensor Products

6. Modules over a Principal Ideal Domain

7. Algebras

V: Fields and Galois Theory

1. Field Extensions

2. The Fundamental Theorem

3. Splitting Fields, Algebraic Closure and Normality

4. The Galois Group of a Polynomial

5. Finite Fields

6. Separability

7. Cyclic Extensions

8. Cyclotomic Extensions

9. Radical Extensions

VI: The Structure of Fields

1. Transcendence Bases

2. Linear Disjointness and Separability

VII: Linear Algebra

1. Matrices and Maps

2. Rank and Equivalence

3. Determinants

4. Decomposition of a Single Linear Transformation and Similarity

5. The Characteristic Polynomial, Eigenvectors and Eigenvalues

VIII: Commutative Rings and Modules

1. Chain Conditions

2. Prime and Primary Ideals

3. Primary Decomposition

4. Noetherian Rings and Modules

5. Ring Extensions

6. Dedekind Domains

7. The Hilbert Nullstellensatz

IX: The Structure of Rings

1. Simple and Primitive Rings

2. The Jacobson Radical

3. Semisimple Rings

4. The Prime Radical; Prime and Semiprime Rings

5. Algebras

6. Division Algebras

X: Categories

1. Functors and Natural Transformations

2. Adjoint Functors

3. Morphisms

List of Symbols.

Other Format:

Printed edition:

ISBN:

9781461261018

Access Restriction:

Restricted for use by site license.