A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.
FREE Two-Day Shipping for Students. Learn more |
| ||||||||||||||||||
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Editorial Reviews
Review
From the reviews of the second edition: "This book certainly has more than enough material for a two-semester algebra course for first-year graduate students. … The balance among various topics will please some instructors more than others." (Miklós Bóna, MathDL, September, 2007) "The book under review is the second edition of the author’s sweeping text originally titled ‘Algebra’ … . All together, the second edition of P. A. Grillet’s standard primer is a masterly, clearly written, comprehensive and self-contained algebra text for graduate students, with a plentiful supply of additional advanced material … . Moreover, the book under review, in its didactically oriented disposition, represents an excellent source for teachers and instructors of graduate courses in abstract algebra as well." (Werner Kleinert, Zentralblatt MATH, Vol. 1122 (24), 2007)
From the Back Cover
"Abstract Algebra" is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standard contents with a careful introduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees of difficulty. For the new edition, the author has completely rewritten the entire text, streamlining the first chapters for rapid access to Galois theory, removing some material, and adding introductions to Groebner bases, Ext and Tor, and other topics. From a review of the First Edition: ...combines an exceptionally accessible discussion of the basic material with a just as thorough and well-organized treatment of the many additional (advanced) topics included.... represents an outstanding introduction to modern abstract algebra as a whole, with many unique features. It captivates the reader by its remarkable diversity, comprehensiveness, elegant succinctness, and coherence. - Werner Kleinert, Zentralblatt
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
9 of 9 people found the following review helpful:
5.0 out of 5 stars
Full of Insight,
By
This review is from: Algebra (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)
This book does not complicate every concept, on the contrary, and for example, this is the only algebra text I am currently aware of that actually provides insight into the 'mechanics' of morphisms between various types of sets. To be precise, in section 1.6 (The Isomorphism Theorems), Grillet, introduces and describes both factoring through a domain and codomain. For the student, this provides insight into what is happening 'behind-the-scenes' in the homomorphism theorem and,in turn, acts as a vehicle that enables the student to fully understand and appreciate the isomorphism theorems. Of course one must take in to account the ability of the student using this text and, given this, I would say Grilet's text requires nothing more than an elementary introduction to the basic algebraic structures. This text is not overwhelmingly wordy like that of Dummit and Foote or baby Hungerford, nor is it stale and lifeless like Lang's. Instead, it is well written, definitely insightful, covers all the material needed at the begining graduate level and this text can be used, like Rotman and Lang's text, as a reference. If this book seems daunting based on the size, then I would recommend either just dealing with it or using Martin Isaacs or Papa Hungerford's since both are complete, challenging and manageable. Enjoy!
7 of 7 people found the following review helpful:
4.0 out of 5 stars
Excellent intermediate text,
By A Customer
This review is from: Algebra (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)
Having used this book in a graduate algebra course, I feel that it is an excellent text for those who have already had a rigorous introductory exposure to modern algebra (say, via Dummit and Foote or Fraleigh). Grillet writes clearly and concisely and leaves several challenging (but doable) proofs to the reader. His wry sense of humor is also reflected in his writing.On some subjects, it is more of a survey of topics (such as category theory, universal algebras, exterior products), the point of which only becomes clear after one needs to use these tools in other areas. If you are new to the subject, however, the texts by Dummit and Foote or Fraleigh, e.g., are more appropriate.
8 of 10 people found the following review helpful:
3.0 out of 5 stars
another good algebra text,
By A Customer
This review is from: Algebra (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Hardcover)
This text is designed for beginning graduate students. The book includes all the basic parts of algebra any mathematician should know. The presentation and proofs are clear and easy to follow. People with no prior exposure to abstract algebra might have problems learning algebra from this book as quite a few important theorems and results are left with no proof. Instructor can easily supplement those missing proofs if he/she thinks that's appropriate. Overall, it's an excellent reference book for researchers, but only a good textbook for students.
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
Key Phrases - Statistically Improbable Phrases (SIPs):
(learn more)
commutative rings, field extensions, principal ideal domains, tower property, factorization theorem, semisimple modules, symmetric groups, exact cohomology sequence, negative connected sequence, directed preordered set, representative irreducible elements, positive connected sequence, adjoint associativity isomorphisms, split coequalizer, closed field whose characteristic, unique module homomorphism, short exact rows, indecomposable subgroups, colimit cone, finite maximal chain, added pointwise, find all extensions, generated ring extension, separating transcendence base, contravariant additive functor Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Structure of Groups, Proof First, Hence Ker, Galois Theory, Proof Assume, Artinian K-algebra, Artinian R-module, Several Variables, One Variable, Therefore Gal, The Krull-Schmidt Theorem, Geometric Constructions, Find Aut, Hilbert's Theorem, Use Theorem, Constructions Proposition, Unique Factorization Domains, Use Hensel, Proof Every, Galois Extensions, Prove Proposition, The Jacobson, The General Linear Group, Cohomology of Groups Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
commutative rings, field extensions, principal ideal domains, tower property, factorization theorem, semisimple modules, symmetric groups, exact cohomology sequence, negative connected sequence, directed preordered set, representative irreducible elements, positive connected sequence, adjoint associativity isomorphisms, split coequalizer, closed field whose characteristic, unique module homomorphism, short exact rows, indecomposable subgroups, colimit cone, finite maximal chain, added pointwise, find all extensions, generated ring extension, separating transcendence base, contravariant additive functor Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Structure of Groups, Proof First, Hence Ker, Galois Theory, Proof Assume, Artinian K-algebra, Artinian R-module, Several Variables, One Variable, Therefore Gal, The Krull-Schmidt Theorem, Geometric Constructions, Find Aut, Hilbert's Theorem, Use Theorem, Constructions Proposition, Unique Factorization Domains, Use Hensel, Proof Every, Galois Extensions, Prove Proposition, The Jacobson, The General Linear Group, Cohomology of Groups Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
So You'd Like to...
|
|
