Basic Notions of Algebra

• Main Author: Shafarevich, Igor R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
• Series: Encyclopaedia of Mathematical Sciences, 11
• Subjects: Mathematics.; K-theory.; Topological groups.; Lie groups.; Topological Groups, Lie Groups.; K-Theory.

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Table of Contents:

• What is Algebra?
• Fields
• Commutative Rings
• Homomorphisms and Ideals
• Modules
• Algebraic Aspects of Dimension
• The Algebraic View of Infinitesimal Notions
• Noncommutative Rings
• Modules over Noncommutative Rings
• Semisimple Modules and Rings
• Division Algebras of Finite Rank
• The Notion of a Group
• Examples of Groups: Finite Groups
• Examples of Groups: Infinite Discrete Groups
• Examples of Groups: Lie Groups and Algebraic Groups
• General Results of Group Theory
• Group Representations
• Some Applications of Groups
• Lie Algebras and Nonassociative Algebra
• Categories
• Homological Algebra
• K-theory.