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The Igusa–Todorov function for comodules

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Abstract

We define the Igusa–Todorov function for left (or right) semiperfect coalgebras. In this context, we prove that a coalgebra is left qcF if and only if its Igusa–Todorov function on right comodules is zero.

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References

  1. Chin, W.: A Brief Introduction to Coalgebra Representation Theory. Lecture Notes in Pure and Applied Mathematics, vol. 237, pp. 109–131. Dekker, New York (2004)

    MATH  Google Scholar 

  2. Dăscălescu, S., Năstăsescu, C., Raianu, S.: Hopf Algebras: An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, vol. 235. Dekker Inc, New York (2001)

    MATH  Google Scholar 

  3. Gómez-Torrecillas, J., Nastascescu, C.: Quasi-co-Frobenius coalgebras. J. Algebra 174, 909–923 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Huard, F., Lanzilotta, M.: Self-injective right artinian rings and Lgusa–Todorov functions. Algebras Represent. Theory 16, 765–770 (2012)

  5. Huard, F., Lanzilotta, M., Mendoza, O.: An approach to the finitistic dimension conjecture. J. Algebra 319(9), 3916–3934 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Igusa, K., Todorov, G.: On finitistic global dimension conjecture for artin algebras. Represent. Algebras Relat. Top. 45, 201–204 (2005)

    MathSciNet  MATH  Google Scholar 

  7. Khurana, D.: Semiperfect rings and Nakayama permutations. Glasg. Math. J. 44, 301–309 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Năstăsescu, C., Torrecillas, B., Van Oystaeyen, F.: When is a Coalgebra a generator. Algebras Represent. Theory 11(2), 179–190 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Simson, D.: Coalgebras, comodules, pseudocompact algebras and tame comodule type. Colloq. Math. 90(1), 101–150 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Marcelo Lanzilotta.

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The authors want to thank ANII-FCE 2007-059, Uruguay.

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Haim, M., Lanzilotta, M. & Mata, G. The Igusa–Todorov function for comodules. São Paulo J. Math. Sci. 11, 59–67 (2017). https://doi.org/10.1007/s40863-016-0045-5

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  • DOI: https://doi.org/10.1007/s40863-016-0045-5

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