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010   $a3-319-11478-6
024 7 $a10.1007/978-3-319-11478-1
035   $a(CKB)3710000000360266
035   $a(EBL)1973832
035   $a(SSID)ssj0001452217
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035   $a(PQKBTitleCode)TC0001452217
035   $a(PQKBWorkID)11479087
035   $a(PQKB)10202038
035   $a(DE-He213)978-3-319-11478-1
035   $a(MiAaPQ)EBC5595352
035   $a(MiAaPQ)EBC1973832
035   $a(Au-PeEL)EBL1973832
035   $a(OCoLC)903048339
035   $a(PPN)184498090
035   $a(EXLCZ)993710000000360266
100   $a20150205d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 13$aAn Invitation to General Algebra and Universal Constructions /$fby George M. Bergman
205   $a2nd ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (574 p.)
225 1 $aUniversitext,$x0172-5939
300   $aDescription based upon print version of record.
311   $a3-319-11477-8 
320   $aIncludes bibliographical references and index.
327   $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.
330   $aRich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
410  0$aUniversitext,$x0172-5939
606   $aAlgebra
606   $aCategory theory (Mathematics)
606   $aHomological algebra
606   $aAssociative rings
606   $aRings (Algebra)
606   $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
615  0$aAlgebra.
615  0$aCategory theory (Mathematics).
615  0$aHomological algebra.
615  0$aAssociative rings.
615  0$aRings (Algebra).
615 14$aGeneral Algebraic Systems.
615 24$aCategory Theory, Homological Algebra.
615 24$aAssociative Rings and Algebras.
676   $a512.9
700   $aBergman$b George M$4aut$4http://id.loc.gov/vocabulary/relators/aut$061852
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299778103321
996   $aInvitation to general algebra and universal constructions$91522508
997   $aUNINA