LEADER 03579nam 22006375 450 001 9910144941703321 005 20200703234738.0 010 $a3-540-48042-0 024 7 $a10.1007/b83849 035 $a(CKB)1000000000233268 035 $a(SSID)ssj0000323306 035 $a(PQKBManifestationID)12132003 035 $a(PQKBTitleCode)TC0000323306 035 $a(PQKBWorkID)10297162 035 $a(PQKB)10266875 035 $a(DE-He213)978-3-540-48042-6 035 $a(MiAaPQ)EBC6301255 035 $a(MiAaPQ)EBC5585683 035 $a(Au-PeEL)EBL5585683 035 $a(OCoLC)1066179141 035 $a(PPN)155170910 035 $a(EXLCZ)991000000000233268 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFrobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations /$fby Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (XIV, 354 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1787 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-43782-7 320 $aIncludes bibliographical references (pages [345]-352) and index. 327 $aPart I: Entwined modules and Doi-Koppinen Hopf modules -- 1. Generalities -- 2. Doi-Koppinen Hopf modules and entwined modules -- 3. Frobenius and separable functors for entwined modules -- 4. Applications -- Part II: Nonlinear equations -- 5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation -- 6. Hopf modules and the pentagon equation -- 7. Long dimodules and the Long equation -- 8. The Frobenius-Separability equation -- References -- Index. 330 $aDoi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1787 606 $aAssociative rings 606 $aRings (Algebra) 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 14$aAssociative Rings and Algebras. 676 $a512.24 700 $aCaenepeel$b Stefaan$4aut$4http://id.loc.gov/vocabulary/relators/aut$059359 702 $aMilitaru$b Gigel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aZhu$b Shenglin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144941703321 996 $aFrobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations$92528850 997 $aUNINA