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000725558 020__ $$a9783319114781$$qelectronic book
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000725558 0247_ $$a10.1007/978-3-319-11478-1$$2doi
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000725558 035__ $$aSP(OCoLC)903048339
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000725558 049__ $$aISEA
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000725558 08204 $$a512$$223
000725558 1001_ $$aBergman, George M.,$$d1943-$$eauthor.
000725558 24513 $$aAn invitation to general algebra and universal constructions$$h[electronic resource] /$$cGeorge M. Bergman.
000725558 250__ $$aSecond edition.
000725558 264_1 $$aCham :$$bSpringer,$$c2015.
000725558 300__ $$a1 online resource (x, 572 pages) :$$billustrations.
000725558 336__ $$atext$$btxt$$2rdacontent
000725558 337__ $$acomputer$$bc$$2rdamedia
000725558 338__ $$aonline resource$$bcr$$2rdacarrier
000725558 4901_ $$aUniversitext ;$$v351
000725558 504__ $$aIncludes bibliographical references and indexes.
000725558 5050_ $$a1 About the course, and these notes -- Part I: Motivation and Examples -- 2 Making Some Things Precise -- 3 Free Groups -- 4 A Cook's Tour -- Part II: Basic Tools and Concepts -- 5 Ordered Sets, Induction, and the Axiom of Choice -- 6 Lattices, Closure Operators, and Galois Connections -- 7 Categories and Functors -- 8 Universal Constructions -- 9 Varieties of Algebras -- Part III: More on Adjunctions -- 10 Algebras, Coalgebras, and Adjunctions -- References -- List of Exercises -- Symbol Index -- Word and Phrase Index.
000725558 506__ $$aAccess limited to authorized users.
000725558 520__ $$aRich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
000725558 588__ $$aDescription based on print version record.
000725558 650_0 $$aAlgebra.
000725558 650_0 $$aAlgebra, Universal.
000725558 77608 $$iPrint version:$$aBergman, George M.$$tInvitation to General Algebra and Universal Constructions.$$b0002 2015$$z3319114778$$w(OCoLC)898455317
000725558 830_0 $$aUniversitext ;$$v351.
000725558 852__ $$bebk
000725558 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-11478-1$$zOnline Access$$91397441.1
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000725558 980__ $$aEBOOK
000725558 980__ $$aBIB
000725558 982__ $$aEbook
000725558 983__ $$aOnline
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