Abstract Algebra: 242 (Graduate Texts in Mathematics, 242) - Softcover

Grillet, Pierre Antoine

Softcover

ISBN 10: 1441924507 ISBN 13: 9781441924506

Publisher: Springer, 2010

Synopsis

The author has completely reworked this superb textbook for a fully updated new edition. He has reorganized many of the sections, and cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as some topology. In all this is a new version of a classic that is now fit for purpose, a key text 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.

About this title

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

 

Edition details

• Publisher: Springer
• Publication date: 2010
• Language: English
• ISBN 10: 1441924507
• ISBN 13: 9781441924506
• Binding: Paperback
• Number of pages: 686