An Invitation to General Algebra and Universal Constructions: Universitext
Autor George M. Bergmanen Limba Engleză Paperback – 5 mar 2015
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Specificații
ISBN-13: 9783319114774
ISBN-10: 3319114778
Pagini: 572
Ilustrații: X, 572 p. 90 illus.
Dimensiuni: 155 x 235 x 32 mm
Greutate: 8.72 kg
Ediția:2nd ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria Universitext
Locul publicării:Cham, Switzerland
ISBN-10: 3319114778
Pagini: 572
Ilustrații: X, 572 p. 90 illus.
Dimensiuni: 155 x 235 x 32 mm
Greutate: 8.72 kg
Ediția:2nd ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria Universitext
Locul publicării:Cham, Switzerland
Public țintă
GraduateCuprins
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.
Recenzii
“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)
Notă biografică
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.
Textul de pe ultima copertă
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.
Caracteristici
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