Format:
Online-Ressource (X, 572 p. 90 illus, online resource)
Edition:
2nd ed. 2015
ISBN:
9783319114781
Series Statement:
Universitext
Content:
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
Content:
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
Note:
Description based upon print version of record
,
1 About the course, and these notesPart 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.
Additional Edition:
ISBN 9783319114774
Additional Edition:
Druckausg. Bergman, George M., 1943 - An invitation to general algebra and universal constructions Cham : Springer, 2015 ISBN 9783319114774
Language:
English
Subjects:
Mathematics
Keywords:
Universelle Algebra
;
Lehrbuch
DOI:
10.1007/978-3-319-11478-1
URL:
Volltext
(lizenzpflichtig)
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