Basic Notions of Algebra (Google eBook)

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Springer Science & Business Media, Mar 30, 2006 - Mathematics - 262 pages
1 Review
This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Comparable in style with Hermann Weyl's evergreen essay The Classical Groups, Shafarevich's new book is sure to become required reading for mathematicians, from beginners to experts.
  

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Review: Basic Notions Of Algebra

User Review  - Joecolelife - Goodreads

An off-hand account of algebra by one of the best authorities of the subject. Recommended as a "serious" pass-time. Read full review

Contents

Preface
4
10 Semisimple Modules and Rings
79
ll Division Algebras of Finite Rank
90
12 The Notion of a Group
96
Finite Groups
108
Infinite Discrete Groups
124
Lie Groups and Algebraic Groups
140
16 General Results of Group Theory
151
17 Group Representations
160
Characters of compact Abelian groups and Fourier series Weyl and Ricci tensors in
174
19 Lie Algebras and Nonassociative Algebra
188
Categories
202
21 Homological Algebra
213
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