Abstract Algebra

ISBN-13: 9781441924506 / Angielski / Miękka / 2010 / 674 str.

Pierre Antoine Grillet

Opis

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.

Recenzje

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)

Spis treści

Groups.- Structure of Groups.- Rings.- Field Extensions.- Galois Theory.- Fields with Orders or Valuations.- Commutative Rings.- Modules.- Semisimple Rings and Modules.- Projectives and Injectives.- Constructions.- Ext and Tor.- Algebras.- Lattices.- Universal Algebra.- Categories.

O autorze

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.

Blurb

"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