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100   $a20150610d2015      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aFundamentals of Hopf Algebras /$fby Robert G. Underwood
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (XIV, 150 p. 21 illus.)
225 1 $aUniversitext,$x0172-5939
300   $aBibliographic Level Mode of Issuance: Monograph
311 08$a3-319-18990-5 
327   $aPreface -- Notation -- 1. Algebras and Coalgebras -- 2. Bialgebras -- 3. Hopf Algebras -- 4. Applications of Hopf Algebras -- Bibliography.
330   $aThis text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras.  The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author?s 2011 publication, An Introduction to Hopf Algebras.  The book may be used as the main text or as a supplementary text for a graduate algebra course.  Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields, and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises.  Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.
410  0$aUniversitext,$x0172-5939
606   $aAssociative rings
606   $aRings (Algebra)
606   $aCommutative algebra
606   $aCommutative rings
606   $aNumber theory
606   $aComputer science?Mathematics
606   $aComputer science$xMathematics
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aMathematical Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M13110
615  0$aAssociative rings.
615  0$aRings (Algebra)
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aNumber theory.
615  0$aComputer science?Mathematics.
615  0$aComputer science$xMathematics.
615 14$aAssociative Rings and Algebras.
615 24$aCommutative Rings and Algebras.
615 24$aNumber Theory.
615 24$aMathematical Applications in Computer Science.
676   $a512.55
700   $aUnderwood$b Robert G$g(Robert Gene),$4aut$4http://id.loc.gov/vocabulary/relators/aut$01270983
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299769703321
996   $aFundamentals of Hopf Algebras$94451426
997   $aUNINA