Algebra (Heftet)

Notes from the Underground

Serie: Cambridge Mathematical Textbooks 

Forfatter:

Forfatter:
Innbinding: Heftet
Utgivelsesår: 2021
Antall sider: 488
Forlag: Cambridge University Press
Språk: Engelsk
Serie:
ISBN/EAN: 9781108958233
Omtale 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 naive set theory.

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