An Invitation to General Algebra and Universal Constructions

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...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Bergman, George M. (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Cham : Springer International Publishing : Imprint: Springer, 2015.
Édition:2nd ed. 2015.
Collection:Universitext,
Sujets:
Universal algebra.
Algebra, Homological.
Associative rings.
Associative algebras.
General Algebraic Systems.
Category Theory, Homological Algebra.
Associative Rings and Algebras.
Accès en ligne:Texto Completo
Table des matières:
  • 1 About the course, and these notes
  • Part I: Motivation and Examples
  • 2 Making Some Things Precise
  • 3 Free Groups
  • 4 A Cook's Tour
  • Part II: Basic Tools and Concepts
  • 5 Ordered Sets, Induction, and the Axiom of Choice
  • 6 Lattices, Closure Operators, and Galois Connections
  • 7 Categories and Functors
  • 8 Universal Constructions
  • 9 Varieties of Algebras
  • Part III: More on Adjunctions
  • 10 Algebras, Coalgebras, and Adjunctions
  • References
  • List of Exercises
  • Symbol Index
  • Word and Phrase Index.

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