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Algebra Algebra by Hungerford

  1. Strongly Recommend

    50.0%
  2. Lightly Recommend

    25.0%
  3. Lightly don't Recommend

    25.0%
  4. Strongly don't Recommend

    0 vote(s)
    0.0%
  1. Feb 3, 2013 #1

    micromass

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    2016 Award


    Table of Contents:
    Code (Text):

    [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]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 4, 2013 #2
    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...
     
  4. Feb 4, 2013 #3
    that was my experience also. that was also my favourite review, although this was the part that I always remembered:
    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.
     
  5. Feb 4, 2013 #4
    In Springer GTM three books are on Algebra, Lang, Roman & this one.can you arrange these three in difficulty order.
     
  6. Feb 4, 2013 #5
    Roman is by far the easiest, and this one seems easier than Lang. Lang also covers more material.
     
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