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Title
An invitation to general algebra and universal constructions [electronic resource] / George M. Bergman.
Edition
Second edition.
ISBN
9783319114781 electronic book
3319114786 electronic book
9783319114774
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource (x, 572 pages) : illustrations.
Item Number
10.1007/978-3-319-11478-1 doi
Call Number
QA150
Dewey Decimal Classification
512
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and indexes.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Universitext ; 351.
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.
