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Abstract Algebra (Graduate Texts in Mathematics) Paperback – November 23, 2010

ISBN-13: 978-1441924506 ISBN-10: 1441924507 Edition: Softcover reprint of hardcover 2nd ed. 2007
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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

 

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Product Details

  • Series: Graduate Texts in Mathematics (Book 242)
  • Paperback: 674 pages
  • Publisher: Springer; Softcover reprint of hardcover 2nd ed. 2007 edition (November 23, 2010)
  • Language: English
  • ISBN-10: 1441924507
  • ISBN-13: 978-1441924506
  • Product Dimensions: 6 x 1.6 x 9 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 3.2 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #4,499,867 in Books (See Top 100 in Books)

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Customer Reviews

3.2 out of 5 stars
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Most Helpful Customer Reviews

13 of 13 people found the following review helpful By Jason Schorn on February 13, 2004
Format: 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!
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9 of 9 people found the following review helpful By A Customer on January 12, 2002
Format: 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.
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10 of 12 people found the following review helpful By A Customer on July 29, 1999
Format: 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.
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