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.
✔ Author(s): Paolo Aluffi
✔ Title: Algebra (Cambridge Mathematical Textbooks)
✔ Rating : 4.9 out of 5 base on (15 reviews)
✔ ISBN-10: 1108958230
✔ ISBN-13: 9781108958233
✔ Language: English
✔ Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
✔ Device compatibles: Android, iOS, PC and Amazon Kindle
Readers' opinions about Algebra by Paolo Aluffi
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What a rollercoaster of emotions! I laughed, cried, and everything in between. The author's ability to evoke such raw feelings is truly commendable. It's a story that will stay with me forever.
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This is a book I'll cherish and recommend to everyone. It touched my soul and made me reflect on life's profound mysteries.
