Algebra Algebra by Hungerford: Thomas Hungerford | Amazon 0387905189

[micromass]

• Author: Thomas Hungerford
• Title: Algebra
• Amazon link: https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20

Table of Contents:

[LIST]
[*] Preface
[*] Acknowledgments
[*] Suggestions on the Use of This Book
[*] Introduction: Prerequisites and Preliminaries
[LIST]
[*] Logic
[*] Sets and Classes
[*] Functions
[*] Relations and Partitions
[*] Products
[*] The Integers
[*] The Axiom of Choice, Order and Zorn's Lemma
[*] Cardinal Numbers
[/LIST]
[*] Groups
[LIST]
[*] Semigroups, Monoids and Groups
[*] Homomorphisms and Subgroups
[*] Cyclic Groups
[*] Cosets and Counting
[*] Normality, Quotient Groups, and Homomorphisms
[*] Symmetric, Alternating, and Dihedral Groups
[*] Categories: Products, Coproducts, and Free Objects
[*] Direct Products and Direct Sums
[*] Free Groups, Free Products, Generators & Relations
[/LIST]
[*] The Structure of Groups
[LIST]
[*] Free Abelian Groups
[*] Finitely Generated Abelian Groups
[*] The Krull-Schmidt Theorem
[*] The Action of a Group on a Set
[*] The Sylow Theorems
[*] Classification of Finite Groups
[*] Nilpotent and Solvable Groups
[*] Normal and Subnormal Series
[/LIST]
[*] Rings
[LIST]
[*] Rings and Homomorphisms
[*] Ideals
[*] Factorization in Commutative Rings
[*] Rings of Quotients and Localization
[*] Rings of Polynomials and Formal Power Series
[*] Factorization in Polynomial Rings
[/LIST]
[*] Modules
[LIST]
[*] Modules, Homomorphisms and Exact Sequences
[*] Free Modules and Vector Spaces
[*] Projective and Injective Modules
[*] Hom and Duality
[*] Tensor Products
[*] Modules over a Principal Ideal Domain
[*] Algebras
[/LIST]
[*] Fields and Galois Theory
[LIST]
[*] Field Extensions
[*] Appendix: Ruler and Compass Constructions
[*] The Fundamental Theorem
[*] Appendix: Symmetric Rational Functions
[*] Splitting Fields, Algebraic Closure and Normality
[*] Appendix: The Fundamental Theorem of Algebra
[*] The Galois Group of a Polynomial
[*] Finite Fields
[*] Separability
[*] Cyclic Extensions
[*] Cyclotomic Extensions
[*] Radical Extensions
[*] Appendix: The General Equation of Degree n
[/LIST]
[*] The Structure of Fields
[LIST]
[*] Transcendence Bases
[*] Linear Disjointness and Separability
[/LIST]
[*] Linear Algebra
[LIST]
[*] Matrices and Maps
[*] Rank and Equivalence
[*] Appendix: Abelian Groups Defined by Generators and Relations
[*] Determinants
[*] Decomposition of a Single Linear Transformation and Similarity.
[*] The Characteristic Polynomial, Eigenvectors and Eigenvalues
[/LIST]
[*]  Commutative Rings and Modules
[LIST]
[*] Chain Conditions
[*] Prime and Primary Ideals
[*] Primary Decomposition
[*] Noetherian Rings and Modules
[*] Ring Extensions
[*] Dedekind Domains
[*] The Hilbert Nullstellensatz
[/LIST]
[*] The Structure of Rings
[LIST]
[*] Simple and Primitive Rings
[*] The Jacobson Radical
[*] Semisimple Rings
[*] The Prime Radical; Prime and Semiprime Rings
[*] Algebras
[*] Division Algebras
[/LIST]
[*] Categories
[LIST]
[*] Functors and Natural Transformations
[*] Adjoint Functors
[*] Morphisms
[/LIST]
[*] List of Symbols
[*] Bibliography
[*] Index
[/LIST]

 

[Sankaku]

My first encounter with Hungerford was stressful, taking a course that was way over my head. Luckily the teacher was excellent. At the time, I found Hungerford extremely terse and somewhat frustrating, since he insists on doing everything in the most abstract generality (he doesn't assume rings have unity, etc.).

However, I now love the book. Once past the first hurdle, it shows itself to be very clear and well organized. It is superb as a reference, but I would recommend supplementary books if you are tackling a part of it you have never seen before. Hungerford won't hold your hand.

Jacobson's Basic Algebra I and II are excellent, but a very different style. I would recommend getting at least BAI since it is an inexpensive Dover, and Jacobson has some superb insights. However, for me, the king of (intro) grad-level algebra books is Aluffi's Algebra, Chapter 0. It is the grad-level equivalent of Pinter.

For Hungerford, I couldn't help but laugh at this review on Amazon...

If you have a doctorate in pure Mathematics, a respectable doctorate that has nothing to do with PDEs and the thesis for which took longer to write on paper than it did to format the pictures to fit the margins, and you want to look up how much of the ring structure of R is inherited by R[x] in under 3 minutes, then this book belongs on your shelf.

 

[fourier jr]

My first encounter with Hungerford was stressful, taking a course that was way over my head. Luckily the teacher was excellent. At the time, I found Hungerford extremely terse and somewhat frustrating, since he insists on doing everything in the most abstract generality (he doesn't assume rings have unity, etc.).

However, I now love the book. Once past the first hurdle, it shows itself to be very clear and well organized. It is superb as a reference, but I would recommend supplementary books if you are tackling a part of it you have never seen before. Hungerford won't hold your hand.

Jacobson's Basic Algebra I and II are excellent, but a very different style. I would recommend getting at least BAI since it is an inexpensive Dover, and Jacobson has some superb insights. However, for me, the king of (intro) grad-level algebra books is Aluffi's Algebra, Chapter 0. It is the grad-level equivalent of Pinter.

For Hungerford, I couldn't help but laugh at this review on Amazon...

that was my experience also. that was also my favourite review, although this was the part that I always remembered:

But learning by it will leave one with at best amusing memories and a nervous twitch. Just for a taste, "This proof has two parts. The first is easy. The second is left to the reader." About half the proofs in the book go like this.

with a lot of the theorems you only get a "sketch of proof" rather than the whole thing, but it generally wasn't too hard to fill in the details, when I came back to this book anyway. & it still wasn't as tough as lang.

 

[Snow-Leopard]

In Springer GTM three books are on Algebra, Lang, Roman & this one.can you arrange these three in difficulty order.

 

[espen180]

Roman is by far the easiest, and this one seems easier than Lang. Lang also covers more material.