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…
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- 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, United Kingdom
- Language:eng
- Publication Date:©2021
Notes
Includes indexes.
The Physical Object
- Description:xv, 472 pages : : illustrations ; : 25 cm.
Edition Identifiers
- ISBN:9781108958233, 1108958230
- oclc:on1225976790
- LC Classification:QA162
- Dewey Decimal:512/.02
Table of Contents
Part I.Rings -- The integers -- Modular arithmetic -- Rings -- The category of rings -- Canonical decomposition, quotients, and isomorphism theorems -- Integral domains -- Polynomial rings and factorization -- Part II.Modules -- Modules and abelian groups -- Modules over integral domains -- Abelian groups -- Part III. Groups -- Groups-preliminaries -- Basic results on finite groups -- Part IV.Fields -- Field extensions -- Normal and separable extensions, and splitting fields -- Gaiosi theory.
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