03214nam a22005175i 4500
978-3-319-11478-1
DE-He213
20180115171621.0
cr nn 008mamaa
150205s2015 gw | s |||| 0|eng d
9783319114781
978-3-319-11478-1
10.1007/978-3-319-11478-1
doi
QA150-272
PBF
bicssc
MAT002010
bisacsh
512
23
Bergman, George M.
author.
An Invitation to General Algebra and Universal Constructions
[electronic resource] /
by George M. Bergman.
2nd ed. 2015.
Cham :
Springer International Publishing :
Imprint: Springer,
2015.
X, 572 p. 90 illus.
online resource.
text
txt
rdacontent
computer
c
rdamedia
online resource
cr
rdacarrier
text file
PDF
rda
Universitext,
0172-5939
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.
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.
Mathematics.
Associative rings.
Rings (Algebra).
Category theory (Mathematics).
Homological algebra.
Algebra.
Mathematics.
General Algebraic Systems.
Category Theory, Homological Algebra.
Associative Rings and Algebras.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9783319114774
Universitext,
0172-5939
http://dx.doi.org/10.1007/978-3-319-11478-1
ZDB-2-SMA
371542
371542
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK