This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.
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Editorial Reviews
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"...a thorough and surprisingly clean-cut survey of the group/ring/field troika which manages to convey the idea of algebra as a unified enterprise." Ian Stewart, New Scientist
Book Description
In addition to many new problems for practice and challenge, this edition of a self-contained graduate text on abstract algebra contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker-Noether theorem.
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Most Helpful Customer Reviews
15 of 16 people found the following review helpful:
4.0 out of 5 stars
too concise in some parts, good elsewhere,
This review is from: Basic Abstract Algebra (Paperback)
I picked this book up at my students' society used bookstore for $10, it turned out to be a pretty good bargain. However, there are some theorems where the authors say something is obvious & I didn't think so. It isn't very often though, the rest of the book is pretty good, and I was a bit surprised because I had only heard of the well-known authors like Gallian, Herstein, Lang, etc. It covers maybe 3 courses worth of material too, including groups, rings, fields, vector spaces & modules, Galois Theory (complete with every possible application!), and more advanced stuff like a separate chapter on modules (in addition to the section with vector spaces), tensor products and principal ideal domains. There are also complete solutions to the odd-numbered problems. This book is surprisingly good except in certain parts, I like it.
9 of 10 people found the following review helpful:
5.0 out of 5 stars
A must for every math library,
By Scott M. Feldman (Rockaway Park, NY USA) - See all my reviews
This review is from: Basic Abstract Algebra (Hardcover)
Bhattacharya is very concise and readable for a very difficult subject, if you are new to abstract algebra. His proofs are complete and expert and his outline is great. Also his problems are useful
4 of 4 people found the following review helpful:
5.0 out of 5 stars
Excellent. Don't get thrown off by "Basic" Abstract Algebra,
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This review is from: Basic Abstract Algebra (Paperback)
This book will get you there if you believe in it. It has examples with solutions and problems with solutions. The only topic that does not have problems with solutions is categories. For this, I have the Hungerford text, and I am presently in the process of finding a better book for this. Otherwise it is the perfect book for self-study.
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Inside This Book
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First Sentence:
The concept of set is fundamental in mathematics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
defective picture tube, defective sound system, nonisomorphic abelian groups, octic group, nonzero nilpotent ideals, nonzero nil ideals, constructible point, nonzero right ideal, constructible number, splitting field, balanced map, nonzero nilpotent elements, ring with unity, maximal normal subgroup, commutative integral domain, rational canonical form, principal right ideal, artinian ring, normal extension, minimal left ideals, left artinian, nonzero homomorphism, different necklaces, nonreal roots, finite separable extension Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Suppose, Example Let, Proof Clearly, Prove Theorem, Proof By Theorem, Proof Obvious, Let Fbe, Proof First New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The concept of set is fundamental in mathematics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
defective picture tube, defective sound system, nonisomorphic abelian groups, octic group, nonzero nilpotent ideals, nonzero nil ideals, constructible point, nonzero right ideal, constructible number, splitting field, balanced map, nonzero nilpotent elements, ring with unity, maximal normal subgroup, commutative integral domain, rational canonical form, principal right ideal, artinian ring, normal extension, minimal left ideals, left artinian, nonzero homomorphism, different necklaces, nonreal roots, finite separable extension Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Suppose, Example Let, Proof Clearly, Prove Theorem, Proof By Theorem, Proof Obvious, Let Fbe, Proof First New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 7
books:
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6
books
cite this book:
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- An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy in Back Matter
- The Theory of Rings by Neal Henry McCoy in Back Matter
- Fields and Rings (Chicago Lectures in Mathematics) by Irving Kaplansky in Back Matter
- Basic Algebra by Paul M. Cohn in Back Matter
- Basic Algebra by William R. Klinger in Back Matter
See all 7 books this book cites
- Comprehensive Mathematics for Computer Scientists 1 by Guerino B. Mazzola in Back Matter (1), and Back Matter (2)
- Ohio University 1804-2004: Spirit Of Singular Place by Betty Hollow in Back Matter
- Introductory Algebraic Number Theory by Saban Alaca on page 234
- Digital and Image Geometry: Advanced Lectures (Lecture Notes in Computer Science) by Gilles Bertrand on page 206
- Modules and Rings by John Dauns in Back Matter
See all 6 books citing this book
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