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Algebra Notes from the Underground

Authors

Paolo Aluffi
, Florida State University
Published 2021

Description

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…

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Key features

  • Treats all standard topics for a first course in detail, moving from rings to modules to groups to fields, which allows for a more gradual entry into the subject
  • Emphasizes a modern perspective, with hints toward category theory, exposing students to advanced topics and preparing them for graduate courses and applications of algebra in other subjects
  • Includes 400+ exercises, with 150 worked-out problems from the main text, and plenty of examples to help students better understand the material
  • Uses a conversational style and strong narrative flow that makes the material easier for students to follow and appreciate as a whole

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