Basic Notions of Algebra

Authors:

ISBN: 978-3-540-61221-6 (Print) 978-3-540-26474-3 (Online)

Table of contents (22 chapters)

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  1. Front Matter

    Pages I-5

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    Book Chapter

    Pages 6-11

    What is Algebra?

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    Book Chapter

    Pages 11-17

    Fields

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    Book Chapter

    Pages 17-23

    Commutative Rings

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    Book Chapter

    Pages 24-33

    Homomorphisms and Ideals

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    Book Chapter

    Pages 33-40

    Modules

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    Book Chapter

    Pages 41-50

    Algebraic Aspects of Dimension

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    Book Chapter

    Pages 50-61

    The Algebraic View of Infinitesimal Notions

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    Book Chapter

    Pages 61-74

    Noncommutative Rings

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    Book Chapter

    Pages 74-79

    Modules over Noncommutative Rings

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    Book Chapter

    Pages 79-90

    Semisimple Modules and Rings

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    Book Chapter

    Pages 90-96

    Division Algebras of Finite Rank

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    Book Chapter

    Pages 96-108

    The Notion of a Group

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    Book Chapter

    Pages 108-124

    Examples of Groups: Finite Groups

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    Book Chapter

    Pages 124-140

    Examples of Groups: Infinite Discrete Groups

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    Book Chapter

    Pages 140-151

    Examples of Groups: Lie Groups and Algebraic Groups

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    Book Chapter

    Pages 151-160

    General Results of Group Theory

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    Book Chapter

    Pages 160-177

    Group Representations

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    Book Chapter

    Pages 177-188

    Some Applications of Groups

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    Book Chapter

    Pages 188-201

    Lie Algebras and Nonassociative Algebra

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    Book Chapter

    Pages 202-213

    Categories

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