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Algebra|Paolo Aluffi

Algebra : Notes from the Underground

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Overview

From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.

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Details

  • ISBN-13: 9781108958233
  • ISBN-10: 1108958230
  • Publisher: Cambridge University Press
  • Publish Date: June 2021
  • Dimensions: 9.4 x 7.8 x 1 inches
  • Shipping Weight: 1.8 pounds
  • Page Count: 488

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