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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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