LOCALLY DYNKIN QUIVERS AND HEREDITARY COALGEBRAS WHOSE LEFT COMODULES ARE DIRECT SUMS OF FINITE DIMENSIONAL COMODULES

REFERENCES

• Auslander , M. 1976 . “ Large Modules Over Artin Algebras ” . In Algebra, Topology and Category Theory 3 – 17 . New York : Academic Press .
   Google Scholar
• Auslander , M. , Reiten , I. and Smalø , S. 1995 . Representation Theory of Artin Algebras; Cambridge Studies in Advanced Mathematics 36 Cambridge : Cambridge University Press .
   Google Scholar
• Chin , W. and Montgomery , S. 1997 . Basic Coalgebras . AMS/IP Studies in Advanced Mathematics , 4 : 41 – 47 .
   Google Scholar
• Chin , W. , Kleiner , M. and Quinn , D. August 2000 . “ Almost Split Sequences for Comodules, ICRA-9 ” . Beijing
   Google Scholar
• Coelho , F.U. , Marcos , E.N. , Merklen , H.A. and Skowroński , A. 1994 . Module Categories with Infinite Radical Square Zero are of Finite Type . Comm. Algebra , 22 : 4511 – 4517 .
   Web of Science ®Google Scholar
• Doi , Y. 1981 . Homological Coalgebra . J. Math. Soc. Japan , 33 : 31 – 50 .
   Web of Science ®Google Scholar
• Drozdowski , G. and Simson , D. 1979 . Quivers of Pure Semisimple Type . Bull. Pol. Acad. Sci. Math , 27 : 33 – 40 .
   Google Scholar
• Dung , N.V. and García , J.L. 2001 . Categories of Locally Finite Representation Type . J. Algebra , to appear
   Web of Science ®Google Scholar
• Fuller , K. 1976 . On Rings Whose Left Modules are Direct Sums of Finitely Generated Modules . Proc. Amer. Math. Soc. , 54 : 39 – 44 .
   Web of Science ®Google Scholar
• Gabriel , P. 1962 . Des Catégories Abéliennes . Bull. Soc. Math. France , 90 : 323 – 448 .
   Google Scholar
• Gabriel , P. and Unzerlegbare Darstellungen , I. 1972 . Manuscripta Math. , 6 : 71 – 103 .
   Web of Science ®Google Scholar
• Gabriel , P. Auslander-Reiten Sequences and Representation-Finite Algebras . Proc. ICRA II, Ottawa, 1979 .
   Google Scholar
• 1980 . Lecture Notes in Math , 831 : 1 – 71 .
   Google Scholar
• García , J.M. , Jara , P. and Merino , L.M. 1996 . “ Decomposition of Locally Finite Modules ” . In Rings, Hopf Algebras and Brauer Groups , September 12–17 Antwerp and Brussels , , Belgium Proceedings of the Fourth Week on Algebra and Algebraic Geometry, SAGA-4
   Google Scholar
• 1998 . “ Lect. Notes Pure Appl. Math. ” . Vol. 197 , 147 – 157 . New York, NY : Marcel Dekker .
   Google Scholar
• García , J.L. and Martínez Hernández , J. 1993 . Purity through Gabriel's Functor Rings . Bull. Soc. Math. Belgique , 45 : 137 – 152 .
   Google Scholar
• García , J.L. and Simson , D. 2000 . “ Structure Theorems for Pure Semisimple Grothendieck Locally PI-categories ” . Preprint
   Google Scholar
• Gómez Torrecillas , J. 1998 . Coalgebras and Comodules Over a Commutative Ring . Rev. Roum. Math. Pure Appl. , 43 : 591 – 603 .
   Google Scholar
• Gómez Torrecillas , J. , Jara , P. and Merino , L. 1996 . Locally Finite Representations of Algebras . Comm. Algebra , 24 : 4581 – 4601 .
   Web of Science ®Google Scholar
• Gómez Torrecillas , J. and Naˇstaˇsescu , C. 1995 . Quasi-co-Frobenius Coalgebras . J. Algebra , 174 : 909 – 923 .
   Web of Science ®Google Scholar
• Castaño Iglesias , F. and Gómez Torrecillas , J. 1998 . Wide Morita Context and Equivalences of Comodule Categories . J. Pure Appl. Algebra , 131 : 213 – 225 .
   Web of Science ®Google Scholar
• Jensen , C.U. and Lenzing , H. 1989 . “ Algebra, Logic and Applications ” . In Model Theoretic Algebra with Particular Emphasis on Fields, Rings, Modules Vol. 2 , New York : Gordon & Breach Science Publishers .
   Google Scholar
• Kelly , G.M. 1964 . On the Radical of a Category . J. Austral. Math. Soc. , 4 : 299 – 307 .
   Google Scholar
• Montgomery , S. 1993 . Hopf Algebras and their Actions on Rings CMBS No. 82, AMS
   Google Scholar
• Naˇstaˇsescu , C. , Torrecillas , B. and Zhang , Y.H. 1996 . Hereditary Coalgebras . Comm. Algebra , 24 : 1521 – 1528 .
   Web of Science ®Google Scholar
• Popescu , N. 1973 . Abelian Categories with Applications to Rings and Modules Academic Press .
   Google Scholar
• Simson , D. 1974 . Functor Categories in which Every Flat Object is Projective . Bull. Pol. Acad. Sci.: Math. , 22 : 375 – 380 .
   Google Scholar
• Simson , D. 1977 . On Pure Global Dimension of Locally Finitely Presented Grothendieck Categories . Fund. Math. , 96 : 91 – 116 .
   Google Scholar
• Simson , D. 1977 . Pure Semisimple Categories and Rings of Finite Representation Type . J. Algebra , 48 : 290 – 296 .
   Web of Science ®Google Scholar
• 1980 . Corrigendum . 67 : 254 – 256 .
   Google Scholar
• Simson , D. 1978 . On Pure Semi-simple Grothendieck Categories, I . Fund. Math. , 100 : 211 – 222 .
   Google Scholar
• Simson , D. 1979 . Categories of Representations of Species . J. Pure Appl. Algebra , 14 : 101 – 114 .
   Google Scholar
• Simson , D. 1980 . On Pure Semi-simple Grothendieck Categories, II . Fund. Math. , 110 : 107 – 116 .
   Google Scholar
• Simson , D. 1981 . Partial Coxeter Functors and Right Pure Semi-simple Hereditary Rings . J. Algebra , 71 : 195 – 218 .
   Web of Science ®Google Scholar
• Simson , D. 1982 . On the Structure of Locally Finite Pure Semisimple Grothendieck Categories . Cahiers de Topologie et Géom. Diff. , 33 : 397 – 406 .
   Google Scholar
• Simson , D. 1992 . Linear Representations of Partially Ordered Sets and Vector Space Categories Algebra, Logic and Applications Vol. 4 , New York : Gordon & Breach Science Publishers .
   Google Scholar
• Simson , D. Dualities and Pure Semisimple Rings . Proc. Conference Abelian Groups, Module Theory and Topology . University of Padova . Lecture Notes in Pure and Appl. Math., Marcel-Dekker: 1998; Vol. 201, 381 388
   Google Scholar
• Simson , D. On Coalgebras of Tame Comodule Type . Beijing Normal University . Proc. International Conference on Representations of Algebras IX, to appear
   Google Scholar
• Simson , D. 2001 . Coalgebras, Comodules, Pseudocompact Algebras and Tame Comodule Type . Colloq. Math. , to appear
   Google Scholar
• Simson , D. and Skowroński , A. 1999 . The Jacobson Radical Power Series of Module Categories and the Representation Type . Bol. Soc. Mat. Mexicana , 5 : 223 – 236 .
   Web of Science ®Google Scholar
• Sweedler , M.E. 1969 . Hopf Algebras New York : Benjamin .
   Google Scholar
• Woodcock , D. 1997 . Some Categorical Remarks on the Representation Theory of Coalgebras . Comm. Algebra , 25 : 2775 – 2974 .
   Web of Science ®Google Scholar
• Zimmermann , W. 1973 . Einige Charakterisierung der Ringe über denen reine Untermoduln direkte Summanden sind . Bayer. Akad. Wiss. Math.-Natur. , : 77 – 79 . Abt. II
   Google Scholar