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  • 1 Nanjing University Department of Mathematics Nanjing 210093 China
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In this paper, we introduce Gorenstein coat comodules and weakly Gorenstein injective (resp. coat) comodules over any coalgebra C. We prove that, for a left semiperfect coalgebra C, a left C-comodule M is (weakly) Gorenstein coat if and only if M is (weakly) Gorenstein injective. Some properties of weakly Gorenstein injective comodules are studied.

  • Asensio, M. J., López Ramos, J. A. and Torrecillas, B., Gorenstein Coalgebras, Acta Math. Hungar., 85 (1999), no. 1–2, 187–198. MR 1713100 (2000k:16045)

  • Brzezinski, T. and Wisbauer, R., Corings and Comodules, London Math. Soc. Lecture Note Ser., 309. Cambridge Univ. Press, (Cambridge, 2003). MR 2012570 (2004k:16093)

  • Dăscălescu, S., Năstăsescu, C. and Raianu, S., Hopf Algebras: An Introduction. Monogr. Textbooks Pure Appl. Math. 235, Marcel Dekker, (New York, 2001). MR 1786197 (2001j:16056)

  • Doi, Y., Homological Coalgebra, J. Math. Soc. Japan, 33 (1981), no. 1, 31–50. MR 0597479 (82g:16014)

    Doi Y. , 'Homological Coalgebra ' (1981 ) 33 J. Math. Soc. Japan : 31 -50.

  • El Bashir, R., Covers and Directed Colimits, Algebr. Represent. Theory, 9 (2006), 423–430. MR 2252654 (2007k:16003)

    Bashir R. , 'Covers and Directed Colimits ' (2006 ) 9 Algebr. Represent. Theory : 423 -430.

  • Enochs, E. E., Injective and Flat Covers, Envelopes and Resolvents, Israel J. Math., 39 (1981), no. 3, 189–209. MR 0636889 (83a:16031)

    Enochs E. E. , 'Injective and Flat Covers, Envelopes and Resolvents ' (1981 ) 39 Israel J. Math. : 189 -209.

    • Search Google Scholar
  • Enochs, E. E. and Jenda, O. M. G., Relative Homological Algebra, de Gruyter Exp. Math. 30, de Gruyter, (Berlin, 2000). MR 1753146 (2001h:16013)

  • Enochs, E. E. and Jenda, O. M. G., Copure Injective Resolutions, Flat Resolvents and Dimensions, Comment. Math. Univ. Carolin, 34 (1993), no. 2, 203–211. MR 1241728 (95e:16007)

    Jenda O. M. G. , 'Copure Injective Resolutions, Flat Resolvents and Dimensions ' (1993 ) 34 Comment. Math. Univ. Carolin : 203 -211.

    • Search Google Scholar
  • Enochs, E. E. and López-Ramos, J. A., Relative Homological Coalgebras, Acta Math. Hungar., 104 (2004), no. 4, 331–343. MR 2082783 (2005e:16062)

    López-Ramos J. A. , 'Relative Homological Coalgebras ' (2004 ) 104 Acta Math. Hungar. : 331 -343.

    • Search Google Scholar
  • Lin, B. I.-p., Semiperfect Coalgebras, J. Algebra, 49 (1977), no. 2, 357–373. MR 0498663 (58#16749)

    Lin B. I.-p. , 'Semiperfect Coalgebras ' (1977 ) 49 J. Algebra : 357 -373.

  • Năstăsescu, C., Torrecillas, B. and Zhang, Y. H., Hereditary Coalgebras, Comm. Algebra, 24 (1996), 1521–1528. MR 1380608 (96m:16057)

    Zhang Y. H. , 'Hereditary Coalgebras ' (1996 ) 24 Comm. Algebra : 1521 -1528.

  • Rotman, J. J., An Introduction to Homological Algebra, Academic Press, (New York, 1979). MR 0636889 (83a:16031)

  • Stenström, B., Direct Sum Decomposition in Grothendieck Categories, Ark. Mat., 7 (1968), 427–432. MR 0246940 (40#209)

    Stenström B. , 'Direct Sum Decomposition in Grothendieck Categories ' (1968 ) 7 Ark. Mat. : 427 -432.

    • Search Google Scholar