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Abstract Algebra [electronic resource] /by Pierre Antoine Grillet.

by Grillet, Pierre Antoine [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Graduate Texts in Mathematics: 242Publisher: New York, NY : Springer New York, 2007.Description: XII, 669 p. online resource.ISBN: 9780387715681.Subject(s): Mathematics | Algebra | Group theory | Mathematics | Algebra | Associative Rings and Algebras | Group Theory and GeneralizationsDDC classification: 512 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: "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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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.

"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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