Algebra

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?e set theory.

Author: Paolo Aluffi
Binding Type: Paperback
Publisher: Cambridge University Press
Published: 07/29/2021
Series: Cambridge Mathematical Textbooks
Pages: 488
Weight: 1.8lbs
Size: 9.40h x 7.80w x 1.00d
ISBN: 9781108958233