Algebra (eBook)

Notes from the Underground

Paolo Aluffi (Autor)

eBook Download: PDF

2021
Cambridge University Press (Verlag)
978-1-108-96269-8 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 7.7.2021
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 1-108-96269-6 / 1108962696
• ISBN-13: 978-1-108-96269-8 / 9781108962698