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  • Textbook
  • © 2007

Abstract Algebra

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  • Unique collection of nonstandard topics

  • Clearly written, succinctly presented

  • Contains numerous interrelations between the various topics discussed

  • Accessible discussion of the basic material, combined with a thorough treatment of many advanced topics

Part of the book series: Graduate Texts in Mathematics (GTM, volume 242)

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  • ISBN: 978-0-387-71568-1
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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xii
  2. Groups

    Pages 1-42
  3. Structure of Groups

    Pages 43-104
  4. Rings

    Pages 105-154
  5. Field Extensions

    Pages 156-190
  6. Galois Theory

    Pages 191-230
  7. Commutative Rings

    Pages 273-314
  8. Modules

    Pages 315-358
  9. Constructions

    Pages 415-462
  10. Ext and Tor

    Pages 463-514
  11. Algebras

    Pages 515-538
  12. Lattices

    Pages 539-558
  13. Universal Algebra

    Pages 559-580
  14. Categories

    Pages 581-624
  15. Back Matter

    Pages 625-669

About this book

"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

 

Keywords

  • Abstract algebra
  • Galois theory
  • Lattice
  • algebra
  • commutative ring

Reviews

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)

Authors and Affiliations

  • Tulane University, 10178, USA

    Pierre Antoine Grillet

Bibliographic Information

Buying options

eBook
USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-71568-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 69.95
Price excludes VAT (USA)
Hardcover Book
USD 69.95
Price excludes VAT (USA)