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An Invitation to General Algebra and Universal Constructions

  • George M. Bergman

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. George M. Bergman
    Pages 1-8
  3. Motivation and Examples

    1. Front Matter
      Pages 9-9
    2. George M. Bergman
      Pages 11-23
    3. George M. Bergman
      Pages 25-44
    4. George M. Bergman
      Pages 45-115
  4. Basic Tools and Concepts

    1. Front Matter
      Pages 117-117
    2. George M. Bergman
      Pages 119-171
    3. George M. Bergman
      Pages 173-212
    4. George M. Bergman
      Pages 213-293
    5. George M. Bergman
      Pages 295-377
    6. George M. Bergman
      Pages 379-454
  5. More on Adjunctions

    1. Front Matter
      Pages 455-455
  6. Back Matter
    Pages 531-572

About this book

Introduction

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Keywords

Galois connections categories; functors coalgebra objects free groups lattices ordered sets universal constructions varieties of algebras

Authors and affiliations

  • George M. Bergman
    • 1
  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11478-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-11477-4
  • Online ISBN 978-3-319-11478-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site