Algebra: Notes from the Underground
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 naïve set theory.
카테고리:
권:
472
년:
2021
판:
1
출판사:
Cambridge University Press
언어:
english
페이지:
425
ISBN 10:
1108962696
ISBN 13:
9781108962698
시리즈:
Cambridge Mathematical Textbooks
파일:
PDF, 3.86 MB
IPFS:
,
english, 2021