03055nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001600165072002300181082001500204100003400219245008400253264007500337300004400412336002600456337002600482338003600508347002400544490002900568505014400597520129300741650001702034650002302051650002102074650002502095650002302120650003502143650002602178650001902204650001702223650003602240650003602276650001902312650005102331710003402382773002002416776003602436830002902472856004802501978-3-319-18991-8DE-He21320180115171634.0cr nn 008mamaa150610s2015 gw | s |||| 0|eng d a97833191899187 a10.1007/978-3-319-18991-82doi 4aQA251.5 7aPBF2bicssc 7aMAT0020102bisacsh04a512.462231 aUnderwood, Robert G.eauthor.10aFundamentals of Hopf Algebrash[electronic resource] /cby Robert G. Underwood. 1aCham :bSpringer International Publishing :bImprint: Springer,c2015. aXIV, 150 p. 21 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext,x0172-59390 aPreface -- Notation -- 1. Algebras and Coalgebras -- 2. Bialgebras -- 3. Hopf Algebras -- 4. Applications of Hopf Algebras -- Bibliography. 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. 0aMathematics. 0aAssociative rings. 0aRings (Algebra). 0aCommutative algebra. 0aCommutative rings. 0aComputer sciencexMathematics. 0aComputer mathematics. 0aNumber theory.14aMathematics.24aAssociative Rings and Algebras.24aCommutative Rings and Algebras.24aNumber Theory.24aMathematical Applications in Computer Science.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783319189901 0aUniversitext,x0172-593940uhttp://dx.doi.org/10.1007/978-3-319-18991-8