Algebra

By Paolo Aluffi

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 na ve set theory.

• Format: Paperback
• Language: English
• ISBN: 1108958230
• ISBN13: 9781108958233
• Release Date: July 2021
• Publisher: Cambridge University Press
• Length: 488 Pages
• Weight: 1.80 lbs.
• Dimensions: 1.0" x 7.8" x 9.4"