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 naive set theory.
- ISBN:
- 9781108958233
- 9781108958233
-
Category:
- Algebra
- Format:
- Paperback
- Publication Date:
-
31-05-2021
- Publisher:
- Cambridge University Press
- Country of origin:
- United Kingdom
- Pages:
- 488
- Dimensions (mm):
- 244x171x27mm
- Weight:
- 0.84kg
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