An Invitation to General Algebra and Universal Constructions

George M. Bergman (Autor)

Buch | Softcover

X, 572 Seiten

2015 | 2nd ed. 2015
Springer International Publishing (Verlag)
978-3-319-11477-4 (ISBN)

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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.

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.

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.

"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)

Erscheint lt. Verlag	5.3.2015
Reihe/Serie	Universitext
Zusatzinfo	X, 572 p. 90 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	861 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Algebra • categories • categories; functors • coalgebra objects • Free Groups • functors • Galois connections • lattices • Ordered sets • universal constructions • varieties of algebras
ISBN-10	3-319-11477-8 / 3319114778
ISBN-13	978-3-319-11477-4 / 9783319114774
Zustand	Neuware