Algebra
Published on 3. December 1980
Book
Hardback
XXIV, 504 pages
978-0-387-90518-1 (ISBN)
Description
"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 accommodate a wide variety of instructors and course contents. It contains an unusually large number of illustrative exercises.
Reviews / Votes
From the book reviews:
"This is a text for a first-year graduate course in abstract algebra. It covers all the standard topics and has more than enough material for a year course." (Allen Stenger, MAA Reviews, September, 2014)
Thomas W. Hungerford
Algebra
"An excellent text from which to teach the beginning graduate survey course in algebra and I would recommend it to anyone considering a text for such a course."- LINEAR AND MULTILINEAR ALGEBRA
More details
Series
Edition
1st Corrected ed. 1974. Corr. 4th printing 2003
Language
English
Place of publication
New York
United States
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
XXIV, 504 p.
Dimensions
Height: 244 mm
Width: 163 mm
Thickness: 38 mm
Weight
981 gr
ISBN-13
978-0-387-90518-1 (9780387905181)
DOI
10.1007/978-1-4612-6101-8
Schweitzer Classification
Other editions
Additional editions
Content
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 & 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 andEquivalence.- 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.