Overview
- Reviews many concrete examples of universal constructions, motivating the development of general algebra and the category-theoretic view of universal constructions
- Enriches the reader's intuition of the abstract theory through many informal discussions
- Provides a large number of engaging exercises
Part of the book series: Universitext (UTX)
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Table of contents (10 chapters)
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Front Matter
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Motivation and Examples
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Front Matter
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More on Adjunctions
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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 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.” (Danica Jakubíková-Studenovská, zbMATH 1317.08001, 2015)
Authors and Affiliations
About the author
George M. Bergman is Professor Emeritus of Mathematics at the University of California, Berkeley. He has published over 100 research articles in logic, ring theory, universal algebra, and category theory.
Bibliographic Information
Book Title: An Invitation to General Algebra and Universal Constructions
Authors: George M. Bergman
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-11478-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-11477-4Published: 05 March 2015
eBook ISBN: 978-3-319-11478-1Published: 05 February 2015
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: X, 572
Number of Illustrations: 90 b/w illustrations
Topics: General Algebraic Systems, Category Theory, Homological Algebra, Associative Rings and Algebras