An invitation to general algebra and universal constructions.
type: Item
instance of: scholarly article
title: An invitation to general algebra and universal constructions.
zbMATH Open document ID: 1317.08001
DOI: 10.1007/978-3-319-11478-1
author: George M. Bergman
published in: Universitext
publication date: 2014-10-01T00:00:00Z
review text: The aim of this book is to survey the basic notions and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. The titles of the chapters are as follows: 1. About the Course and These Notes, 2. Motivation and Examples, 3. Free Groups, 4. A Cook's Tour of Other Universal Constructions, 5. Ordered Sets, Induction, and the Axiom of Choice, 6. Lattices, Closure Operators, and Galois Connections, 7. Categories and Functors, 8. Universal Constructions in Category-Theoretic Terms, 9. Varieties of Algebras, 9. Algebra and Coalgebra Objects in Categories, and Functors Having Adjoints. The author goes along with a reader, shows a motivation and a lot of examples and exercises, leads him to get a common view over several branches of algebra and other disciplines, investigating well-known and some less known constructions. The fundamental part of the book is contained in Chapters 7-10, where a category-theoretic approach is applied. The author takes care in writing full proofs throughout the book and he shows also ways of possible applications. The text contains a wealth material and should serve as a textbook for readers interested in this field. For a review of the first ed. [Berkeley, CA: Henry Helson (1998)] see Zbl 0917.00001.
Mathematics Subject Classification ID: 08-01
Mathematics Subject Classification ID: 18-01
Mathematics Subject Classification ID: 08A02
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 18Axx
zbMATH DE Number: 6350970
zbMATH Keywords: general algebra
zbMATH Keywords: universal algebra
zbMATH Keywords: free groups
zbMATH Keywords: universal constructions
zbMATH Keywords: ordered sets
zbMATH Keywords: lattices
zbMATH Keywords: Galois connections
zbMATH Keywords: categories
zbMATH Keywords: functors
zbMATH Keywords: varieties of algebras
zbMATH Keywords: coalgebra objects
reviewed by: Danica Jakubiková-Studenovská
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-11478-1
OpenAlex ID: W361203971
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description: scientific article; zbMATH DE number 6350970