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…
Read More ↓Title Statements
- Full title :Algebra / Paolo Aluffi.
Summary
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 naïve set theory.
Read More ↓Edition Statements
- Publication Date:2021.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:zxx
- Publication Date:2021.
The Physical Object
- Description:1 online resource (xv, 471 pages)
Edition Identifiers
- ISBN:9781108955911, 1108955916
- oclc:on1264878492
- LC Classification:QA152
- Dewey Decimal:512/.02
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