An Invitation to General Algebra and Universal Constructions

• Κύριος συγγραφέας: Bergman, George M. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Έκδοση: 2nd ed. 2015.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Associative rings.; Rings (Algebra).; Category theory (Mathematics).; Homological algebra.; Algebra.; General Algebraic Systems.; Category Theory, Homological Algebra.; Associative Rings and Algebras.

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...

Πίνακας περιεχομένων:

• 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.