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When is a Coalgebra a Generator?

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Abstract

Let C be a coalgebra over a field k. The aim of this paper is to study the following problem : (P) If C is a k-coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical series, the answer is positive.

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References

  1. Castaño, F., Chifan, N., Năstăsescu, C.: Localizations on certain Grothendieck categories (submitted)

  2. Castaño, F., Dăscălescu, S., Năstăsescu, C.: Symmetrical coalgebras. J. Algebra 279, 326–344 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dăscălescu, S.: Some examples of integral for bialgebras (preprint)

  4. Dăscălescu, S., Năstăsescu, C., Raianu, S.: Hopf Algebras, An introduction. Marcel Dekker, New York (2001)

    Google Scholar 

  5. Gabriel, P.: Des categories abeliennes. Bull. Soc. Math. France 90, 323–448 (1062)

    MathSciNet  Google Scholar 

  6. Gómez-Torrecillas, J., Manu, C., Năstăsescu, C.: Quasi-co-Frobenius coalgebras II. Comm. Algebra 31(10), 5169–5177 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gómez-Torrecillas, J., Năstăsescu, C., Torrecillas, B.: Localization in coalgebras. Applications to finiteness condition. J. Algebra its Applications 6(2), 233–243 (2007)

    Article  MATH  Google Scholar 

  8. Harada, M.: Perfect categories I. Osaka J. Math. 10, 329–341 (1973)

    MATH  MathSciNet  Google Scholar 

  9. Năstăsescu, C.: A generalization of Gabriel–Popescu Theorem (preprint)

  10. Năstăsescu, C.: Théorème de Hopkins pour les catégories de Grothendieck. In: Ring Theory, Antwerp 1980. Lecture Notes, vol. 825. Springer, Berlin

  11. Năstăsescu, C., Torrecillas, B., Zhang, Y.: Hereditary coalgebras. Comm. Algebra 24, 1521–1528 (1996)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Bucharest, Faculty of Mathematics, Str. Academiei 14, RO-70109, Bucharest 1, Romania

    C. Năstăsescu

  2. Departamento de Algebra y Análisis, Universidad de Almería, 04071, Almeria, Spain

    B. Torrecillas

  3. Department of Mathematics, University of Antwerp, Middelheimcampus, Antwerp, Belgium

    F. Van Oystaeyen

Authors
  1. C. Năstăsescu
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  2. B. Torrecillas
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  3. F. Van Oystaeyen
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Correspondence to C. Năstăsescu.

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Năstăsescu, C., Torrecillas, B. & Van Oystaeyen, F. When is a Coalgebra a Generator?. Algebr Represent Theor 11, 179–190 (2008). https://doi.org/10.1007/s10468-007-9054-5

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  • DOI: https://doi.org/10.1007/s10468-007-9054-5

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