Finally 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. The guiding principle throughout is that the material should be presented as general as possible, consistent with good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.
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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
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Most Helpful Customer Reviews
40 of 42 people found the following review helpful:
5.0 out of 5 stars
Well worth the read for any budding mathematician,
By Todd Ebert (Long Beach California) - See all my reviews
This review is from: Algebra (Graduate Texts in Mathematics) (v. 73) (Hardcover)
I've been acquainted with several introductory graduate algebrabooks over the years, and prefer this one for its coverage of all the fundamental areas (groups, modules, rings, linear algebra, fields, and category theory), being concise, and providing great care when outlining each proof. If one compare's the amount of material in this book to Jacobson's "Basic Algebra Vol 1", Grove's "Algebra", or Herstein's "Abstract Algebra", Hungerford's book gets the nod. One last good word about this book: I found the exercises both in abundance (after each section) and quite reasonable for a first year grad. student. Happy reading.
20 of 20 people found the following review helpful:
4.0 out of 5 stars
Encyclopedic, but dry.,
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This review is from: Algebra (Graduate Texts in Mathematics) (v. 73) (Hardcover)
This tome is probably the best single-volume REFERENCE for basic abstract algebra at the graduate level. It touches on almost every important subject. However, the style is very much in the way of an efficient, concise, statement of fact rather than a lucid expository of subject-matter.This is an excellent reference, but for the task of learning the material (especially if without a lecture), I would recommend Dummit and Foote or Steinbeck (the former for advanced undergraduate, the latter for purely graduate study). Also, while this is very comprehensive, it simply cannot fully treat everything in all subjects. For example, very little is given in the way of group (co)homology. For the specialist, you should instead invest in more specific books (e.g. Robinson).
18 of 18 people found the following review helpful:
4.0 out of 5 stars
Impressive, if not so easy to read,
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This review is from: Algebra (Graduate Texts in Mathematics) (v. 73) (Hardcover)
As a reference, this is simply an amazing book; tons of information are crammed into this book. The flip side is that if you are seeing this information for the first time, the presentation can be a little daunting. I started using this book in a class last year and hated it at first, because the presentation of material here is very densely packed together and not written for maximum clarity. For example, the chapter on category theory was the first time I'd seen the subject, and I found it frustrating, unlike the presentation given by, say, Rotman in his Algebraic Topology text. All of that said, though, I appreciate the book more now looking back on the material. Overall, if you haven't seen the material before, this is a fine book as long as you've got someone to help you through the rough spots. As a reference, though, this book is extraordinary.
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Inside This Book
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First Sentence:
In Sections 1-6 we summarize for the reader's convenience some basic material with which he is assumed to be thoroughly familiar (with the possible exception of the distinction between sets and proper classes (Section 2), the characterization of the Cartesian product by a universal mapping property (Theorem 5.2) and the Recursion Theorem 6.2). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
invariant dimension property, left primitive ideals, distinct proper divisors, left quotient ring, solvable series, integral extension ring, transcendence base, weak direct product, regular left ideal, normal endomorphism, reduced primary decomposition, regular maximal, semiprime rings, primitive rings, linear disjointness, commutative ring with identity, primary submodule, multiplicative subset, functor home, subnormal series, nonzero prime ideal, splitting field, algebraic algebra, division ring, finite dimensional extension Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Axiom of Choice, Recursion Theorem, Eisenstein's Criterion, First Isomorphism Theorem, Goldie's Theorem, Lagrange's Theorem, Schroeder-Bernstein Theorem, Artinian K-algebra, Nakayama's Lemma, Cauchy's Theorem, Chinese Remainder Theorem, Binomial Theorem, The Z-module, Third Isomorphism Theorem, Wedderburn-Artin Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In Sections 1-6 we summarize for the reader's convenience some basic material with which he is assumed to be thoroughly familiar (with the possible exception of the distinction between sets and proper classes (Section 2), the characterization of the Cartesian product by a universal mapping property (Theorem 5.2) and the Recursion Theorem 6.2). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
invariant dimension property, left primitive ideals, distinct proper divisors, left quotient ring, solvable series, integral extension ring, transcendence base, weak direct product, regular left ideal, normal endomorphism, reduced primary decomposition, regular maximal, semiprime rings, primitive rings, linear disjointness, commutative ring with identity, primary submodule, multiplicative subset, functor home, subnormal series, nonzero prime ideal, splitting field, algebraic algebra, division ring, finite dimensional extension Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Axiom of Choice, Recursion Theorem, Eisenstein's Criterion, First Isomorphism Theorem, Goldie's Theorem, Lagrange's Theorem, Schroeder-Bernstein Theorem, Artinian K-algebra, Nakayama's Lemma, Cauchy's Theorem, Chinese Remainder Theorem, Binomial Theorem, The Z-module, Third Isomorphism Theorem, Wedderburn-Artin Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
See all 100 books this book cites
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) by Emil Artin on page 251, and Back Matter
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