Rational Modules for Corings

References

• Abuhlail, J. Y. On the Linear Weak Topology and Dual Pairings over Rings. Preprint math. RA/0306356
   Google Scholar
• Abuhlail, J. Y. (2001a). Dualitätstheoreme for Hopf-Algebren über Ringen. Ph.D. dissertation, Heinrich-Heine Universität, Düsseldorf, Germany. (http://www.ulb.uni-duesseldorf.de/diss/ mathnat/2001/abuhlail.html)
   Google Scholar
• Abuhlail , J. Y. , Gómez-Torrecillas , J. and Lobillo , F. 2001b . Duality and rational modules for Hopf algebras over commutative rings . J. Algebra , 240 : 165 – 184 .
   Google Scholar
• Allen , H. and Trushin , D. 1978 . Coproper coalgebras . J. Algebra , 54 : 203 – 215 .
   Google Scholar
• Albu , T. and Wisbauer , R. 1997 . M-density, M-adic completion and M-subgeneration . Rend. Semin. Mat. Univ. Padova , 98 : 141 – 159 .
   Google Scholar
• Berning, J. (1994). Beziehungen zwischen links-linearen Toplogien und Modulkategorien. Dissertation, Heinrich-Heine Universität, Düsseldorf – Germany
   Google Scholar
• Bourbaki , N. 1974 . Elements of Mathematics, Algebra I , Chapters 1–3 Hermann .
   Google Scholar
• Brzeziński , T. The structure of corings. Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties . Algebr. Represent. Theory. , 5 389 – 410 .
   Google Scholar
• Brzeziński , T. 1999 . On modules associated to coalgebra Galois extensions . J. Algebra , 215 : 290 – 317 .
   Google Scholar
• Brzeziński , T. and Majid , S. 1998 . Coalgebra bundles . Comm. Math. Phys. , 191 : 467 – 492 .
   Google Scholar
• Cai , C. and Chen , H. 1994 . Coactions, smash products and Hopf modules . J. Algebra , 167 : 85 – 89 .
   Google Scholar
• Caenepeel , S. , Militaru , G. and Zhu , S. 2002 . Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations , Lect. Not. Math. 1787 Berlin : Springer-Verlag .
   Google Scholar
• Dăscălescu , S. , Năstăsescu , C. and Raianu , Ş . 2001 . Hopf Algebras: An Introduction , Pure App. Mathematics 235 New York : Marcel Dekker .
   Google Scholar
• Doi , Y. 1983 . On the structure of relative Hopf modules . Comm. Algebra , 11 : 243 – 255 .
   Google Scholar
• Doi , Y. 1992 . Unifying Hopf modules . J. Algebra , 153 : 373 – 385 .
   Google Scholar
• Doi , Y. 1994 . “ Generalized smash products and Morita contexts for arbitrary Hopf algebras ” . In Advances in Hopf Algebras , Lect. Notes Pure Appl. Math. 158 Edited by: Bergen , J. et al. 39 – 53 . New York : Marcel Dekker .
   Google Scholar
• El Kaoutit , L. , Gómez-Torrecillas , J. and Lobillo , F. J. Semisimple corings . Algebra Colloquium , To appear
   Google Scholar
• Garfinkel , G. 1976 . Universally torsionless and trace modules . J. Amer. Math. Soc. , 215 : 119 – 144 .
   Google Scholar
• Gómez-Torrecillas , J. 1998 . Coalgebras and comodules over a commutative ring . Rom. J. Pure Appl. Math. , 43 : 591 – 603 .
   Google Scholar
• Gómez-Torrecillas , J. and Năstăsescu , C. 1995 . Quasi-co-Frobenius coalgebras . J. Algebra , 174 : 909 – 923 .
   Google Scholar
• Guzman F. (1985). Cointegratin and Relative Cohomology for Comodules. Ph.D. dissertation, Syracuse University, USA
   Google Scholar
• Guzman , F. 1989 . Cointegrations, relative cohomology for comodules and coseparable corings . J. Algebra , 126 : 211 – 224 .
   Google Scholar
• Köthe , G. 1966 . Topologische lineare Räume I , Die Grundlagen der Mathematischen Wissenschaften 107 Berlin : Springer-Verlag .
   Google Scholar
• Koppinen , M. 1992 . A duality theorem for crossed products of Hopf algebras . J. Algebra , 146 : 153 – 174 .
   Google Scholar
• Koppinen , M. 1995 . Variations on the smash product with applications to group-graded rings . J. Pure Appl. Algebra , 104 : 61 – 80 .
   Google Scholar
• Menini , C. and Zuccoli , M. 1997 . Equivalence theorems and Hopf-Galois extensions . J. Algebra , 194 : 245 – 274 .
   Google Scholar
• Menini , C. , Seidel , A. , Torrecillas , B. and Wisbauer , R. 2001 . A-H-bimodules and equivalences . Comm. Algebra , 29 : 4619 – 4640 .
   Google Scholar
• Menini , C. , Torrecillas , B. and Wisbauer , R. 2001 . Strongly rational comodules and semiperfect Hopf algebras over QF rings . J. Pure Appl. Algebra , 155 : 237 – 255 .
   Google Scholar
• Nichols , W. and Sweedler , M. 1982 . Hopf algebras and combinatorics . Contemp. Math. , 6 : 49 – 84 .
   Google Scholar
• Radford , D. 1973 . Coreflexive coalgebras . J. Algebra , 26 : 512 – 535 .
   Google Scholar
• Schauenburg , P. 2000 . Doi-Koppinen Hopf modules versus entwined modules . New York J. Math. , 6 : 325 – 329 .
   Google Scholar
• Schubert , H. 1972 . Categories Springer-Verlag .
   Google Scholar
• Sweedler , M. 1969 . Hopf Algebras New York : Benjamin .
   Google Scholar
• Sweedler , M. 1975 . The predual theorem to the Jacobson-Bourbaki theorem . Trans. Amer. Math. Soc. , 213 : 391 – 406 .
   Google Scholar
• Tambara , D. 1990 . The coendomorphism bialgebra of an algebra . J. Fac. Sci., Univ. Tokyo, Sect. I A , 37 : 425 – 456 .
   Google Scholar
• Wisbauer , R. 1988 . Grundlagen der Modul- und Ringtheorie München : Verlag Reinhard Fischer . (English edition. (1991). Foundations of Module and Ring Theory. Gordon and Breach, Reading)
   Google Scholar
• Wisbauer , R. 1999 . “ Semiperfect coalgebras over rings ” . In Algebra and Combinatorics , Papers from the International Congress ICAC'97 Hongkong Edited by: Shum , K.-P. 487 – 512 . Singapore : Springer-Verlag .
   Google Scholar
• Wisbauer , R. 2001 . Weak corings . J. Algebra , 245 : 123 – 160 .
   Google Scholar
• Wisbauer , R. On the category of comodules for corings . Proc. 3rd. Int. Pal. Conf.: Math. & Math. Edu. Bethlehem (Palestine). Edited by: Elaydi , S. et al. pp. 325 – 336 . New Jersy : World Scientific . ISBN 981-02-4720-6
   Google Scholar
• Wischnewsky , M. 1975 . On linear representations of affine groups. I . Pac. J. Math. , 61 : 551 – 572 .
   Google Scholar
• Zimmermann-Huisgen , B. 1976 . Pure submodules of direct products of free modules . Math. Ann. , 224 : 233 – 245 .
   Google Scholar