Overview
- 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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Table of contents (16 chapters)
Keywords
About this book
About the first edition:
“The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience.” (Alberto Delgado, MathSciNet)
“This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories.” (Werner Kleinert, Zentralblatt)
For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.
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
Bibliographic Information
Book Title: Abstract Algebra
Authors: Pierre Antoine Grillet
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-71568-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2007
Hardcover ISBN: 978-0-387-71567-4Published: 24 July 2007
Softcover ISBN: 978-1-4419-2450-6Published: 23 November 2010
eBook ISBN: 978-0-387-71568-1Published: 21 July 2007
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XII, 674
Additional Information: Originally published by Wiley, 1999
Topics: Algebra, Associative Rings and Algebras, Group Theory and Generalizations